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WorksheetsAP Statistics Midterm Review
Total questions: 178
Worksheet time: 5hrs 18mins
Country A: 100, 125, 130, 165, 205
About what percent of Country A women weigh between 125 and 205 pounds?
What is the standardized score (z-score) for a student who scored 530 on the old SAT scale?
Here are the ages of randomly selected people at a community playground
3, 10, 42, 25, 5, 8, 6, 12, 15, 4, 3, 21
To make a stemplot of this data you would use the stems
0 and 1
1, 2, and 4
0, 1, 2, 3, and 4
3, 10, 42, 25, 5, 8, 6, 12, 15, 4, 3, and 21
none of the above is a correct answer
If a distribution is symmetrical, which of the following is true?
the mean must be less than the median
the mean and median must be equal
the mean must be greater than the median
the mean is either equal to or less than the median
it's impossible to tell which of the above statements is true without seeing the data
A
B
C
D
E
A
B
C
D
E
The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Bella is at the 87th percentile in height for adult women, then her height, in inches, is closest to
63
67
66
72
70
At a college the scores on the Spanish final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the Humanities final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the Spanish final and 84 on the Humanities final. Relative to the students in each respective class, in which subject did this student do better?
The student did better in Spanish.
The student did better in Humanities.
There is no basis for comparison, since the subjects are different from each other and are in different departments.
The student did equally well in each course.
There is not enough information for comparison.
Which of the following is NOT a measure of spread?
IQR
Mean
Standard Deviation
Range
Some descriptive statistics for a set of test scores are shown above. For this test, a certain student has a standardized score of z = -1.2. What score did this student receive on the test?
266.28
779.42
1008.02
1083.38
1311.98
The boxplots above summarize two data sets, A and B.
Which of the following must be true?
I. Set A contains more data than Set B.
II. The box of Set A contains more data than the box of Set B.
III. The data in Set A have a larger range than the data in Set B.
I only
III only
I and II only
II and III only
I, II, and III
At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the chemistry final and 84 on the calculus final. Relative
to the students in each respective class, in which subject did this student do better?
The student did better in chemistry.
The student did better in calculus.
The student did equally well in each course.
There is no basis for comparison, since the subjects are different from each other and are in different
departments.
There is not enough information for comparison, because the number of students in each class is not
known.
A random sample of 374 United States pennies was collected, and the age of each penny was determined.
According to the boxplot below, what is the approximate interquartile range (IQR) of the ages?
8
10
16
40
50
The histogram below displays the frequencies of waiting times, in minutes, for 175 patients in a dentist's office.
Which of the following could be the median of the waiting times, in minutes?
2.5
7.25
12.25
15
17.50
The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds.
Approximately, what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds?
276 pounds
324 pounds
330 pounds
340 pounds
530 pounds
For a sample of 42 rabbits, the mean weight is 5 pounds and the standard deviation of weights is 3 pounds.
Which of the following is most likely true about the weights for the rabbits in this sample?
The distribution of weights is approximately normal because the sample size is 42, and therefore the central limit theorem applies.
The distribution of weights is approximately normal because the standard deviation is less than the mean.
The distribution of weights is skewed to the right because the least possible weight is within 2 standard deviations of the mean.
The distribution of weights is skewed to the left because the least possible weight is within 2 standard deviations of the mean.
The distribution of weights has a median that is greater than the mean.
The histogram above shows the number of minutes needed by 45 students to finish playing a computer game.
Which of the following statements is correct?
The distribution is skewed to the right.
The distribution is skewed to the left.
The distribution appears to be normal.
The distribution appears to be chi-square.
The distribution appears to be uniform.
Of the following dotplots, which represents the set of data that has the greatest standard deviation?
Which of the following histograms has a shape that is approximately uniform?
Data were collected on the amount, in dollars, that individual customers spent on dinner in an Italian restaurant. The quartiles for these data are given in the picture.
Which of the following statements must be true for these customers?
At least half of the customers spent less than or equal to $44.27 and at least half spent greater than or equal to $44.27.
Seventy-five percent of the customers spent between $36.27 and $58.97.
Twenty-five percent of the customers spent less than or equal to $58.97 and the remaining 75 percent spent greater than or equal to $58.97.
The mean amount spent by customers is $44.27.
A majority of customers spent $44.27.
The back-to-back stem-and-leaf plot below gives the percentage of students who dropped out of school at each of the 49 high schools in a large metropolitan school district.
Which of the following statements is NOT justified by these data?
The drop-out rate decreased in each of the 49 schools between the 1989-90 and 1992-1993 school years.
For the school years shown, most students in the 49 schools did not drop out of high school.
In general drop-out rates decreased between the 1989-90 and 1992-1993 school years.
The median drop-out rate of the 49 high schools decreased between the 1989-90 and 1992-1993 school years.
The spread between the schools with the lowest drop-out rates and those with the highest drop-out rates did not change much between the 1989-90 and 1992-1993 school years.
Gina's doctor told her that the standardized score (z- score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.50.
Which of the following is the best interpretation of this standardized score?
Gina's systolic blood pressure is 150.
Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.
Gina's systolic blood pressure is 1.50 above the average systolic blood pressure of women her age.
Gina's systolic blood pressure is 1.50 times the average systolic blood pressure for women her age.
Only 1.5% of women Gina's age have a higher systolic blood pressure than she does.
For which of the following distributions is the mean greater than the median?
The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.?
0.16
0.32
0.50
0.84
1.00
The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal
distribution. Based on a very large sample, it was found that 10 percent of the loaves weighed less than 15.34
ounces, and 20 percent of the loaves weighed more than 16.31 ounces. What are the mean and standard deviation of
the distribution of the weights of the loaves of bread?
μ = 15.82,
σ = 0.48
μ = 15.82,
σ = 0.69
μ = 15.87,
σ = 0.50
μ = 15.93,
σ = 0.46
μ = 16.00,
σ = 0.50
For a certain population of penguins, the distribution of weight is approximately normal with mean 15.1 kilograms (kg) and standard deviation 2.2 kg. Approximately what percent of the penguins from the population have a weight
between 13.0 and 16.5?
17%
34%
57%
68%
74%
The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult women, then her height, in inches, is closest to
60
62
68
70
74
A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed
and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correction was made?
Mean
Median
Mode
Range
Variance
Which of the following is the best estimate of the standard deviation of the distribution shown in the figure above?
5
10
30
50
60
The fraction of the variation in the values of y that is explained by the least-squares regression of y on x is
the correlation
the slope of the least-squares regression line
the square of the correlation coefficient
the intercept of the least-squares regression line
the residual
Of those whose favorite sport to watch on television is football, what fraction are males?
40/81
52/81
40/52
52/81
12/40
If the point with the red x is removed from the scatterplot, what will happen to the slope of the LSRL and the correlation coefficient?
slope increases, r increases
slope decreases, r increases
slope increases, r decreases
slope decreases, r decreases
slope is unchanged, r increases
Measurements on young children in Mumbai, India, found this least-squares line for predicting height (cm) y from arm span (cm) x: y-hat = 6.4 + 0.93x
According to the regression line, the predicted height of a child with an arm span of 100 cm is about106.4 cm
99.4 cm
93 cm
15.7 cm
7.33 cm
Does the residual plot support the appropriateness of a linear model?
Yes because the residual plot has no apparent pattern
Yes because half the residuals are positive and half are negative
No because points appear to be randomly distributed
No because some points are close to the line when others are not
Yes, because as age increases, the residuals increase
What can you know from the relative frequency graph?
The same amount of people were in each continent in 2011 (orange)
More people were in Asia in 2012
More people were in North America overall
More people were in North America in 2010
A greater percentage of people were in North America than the other continents in 2010
For a biology project, you measure the weight in grams (g) and the tail length in millimeters (mm) of a group of mice. The equation of the least-squares line for predicting tail length from weight is predicted tail length = 20 + 3*weight Which of the following is NOT correct?
The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length.
The predicted tail length of a mouse that weighs 39 grams is 137 millimeters.
By looking at the equation of the least-squares line, you can see that the correlation between weight and tail length is positive.
If you had measured the tail length in centimeters instead of millimeters, the slope of the regression line would have been 3/10 = 0.3
One mouse weighed 29 grams and had a tail length of 100 millimeters. The residual for this mouse is -7.
What is the value of the correlation coefficient?
0.891
-0.891
0.875
0.943
-0.943
Describe the mean and median of this distribution.
Due to the skew, the mean is greater than the median
Due to the skew, the median is greater than the mean
The median is equal to the mean
The mean cannot be estimated from the histogram, but the median can
The median cannot be estimated from the histogram, but the mean can
Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110. In 2009, the mean was 515 and the standard deviation was 116. Jane took the SAT in 1994 and scored 500. Her sister Colleen took the SAT in 2009 and scored 530. Who did better on the exam, and how can you tell?
Colleen - she scored 30 points higher than Jane
Colleen - her standardized score in higher than Jane's
Jane - her standardized score is higher than Colleen's
Jane - the standard deviation was bigger in 2009
The two sisters did equally well - their z-scores are the same
In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was yˆ =10+0.9x where y is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?
85.5
90
9
95.5
none of these
In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was yˆ =10+0.9x where y is the final-exam score and x is the score on the first test. Bill scored a 90 on the first test and a 93 on the final exam. What is the value of his residual?
–2.0
2.0
3.0
93
none of these
A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is y-hat= 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements must be true?
For each one-point increase in performance rating, the raise will increase on average by $1400.
The actual relationship between salary raises and performance rating is linear.
The residuals for half the observations in the dataset will be positive.
The correlation between salary raise and performance rating is negative.
If the mean performance rating is 1.2, then the mean raise is $3800.
A least-squares regression line for predicting weights of basketball players on the basis of their heights produced the residual plot below. What does the residual plot tell you about the linear model?
A residual plot is not an appropriate means for evaluating a linear model.
The curved pattern in the residual plot suggests that there is no association between the weight and height of basketball players.
The curved pattern in the residual plot suggests that the linear model is not appropriate.
There are not enough data points to draw any conclusions from the residual plot.
The linear model is appropriate, because there are approximately the same number of points above and below the horizontal line in the residual plot.
One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: The least-squares regression line is the line that
minimizes the sum of the distances between the actual UV values and the predicted UV values.
minimizes the sum of the squared residuals between the actual yield and the predicted yield.
minimizes the sum of the distances between the actual yield and the predicted UV.
minimizes the sum of the squared residuals between the actual UV reading and the predicted UV values.
minimizes the perpendicular distance between the regression line and each data point.
The equation y=−26.16 + 1.58x can be used to predict a student's heart rate after a brisk walk around the school, if their resting heart rate (before the walk) is known. Suppose a student's resting heart rate is 65 bpm, and after the walk their heart rate is 80 bpm. What is the residual for this student?
76.54
3.46
-3.46
-76.54
The correlation (r) between high school students' height (in inches) and weight (in pounds) for a large sample of students is found to be 0.3. If the weight measurements are converted to kg, what will be the resulting correlation?
(1 kg = 2.2 lbs)
0.3
0.66
-0.3
0.136
Data is obtained for a large group of college students relating the time they spent writing an essay and the grade on the essay. The equation is
grade = 30.18 + 6.49(time) with r = 0.724
What percentage of the variation in grades can be explained by looking at time spent on the essay?
52.4%
72.4%
27.6%
47.6%
Interpret the circled point on this relative cumulative frequency graph.
60% of Starbucks drinks have 30g of sugar.
60% of Starbucks drinks have 30g of sugar or more.
60% of Starbucks drinks have 30g of sugar or less
None of these interpretations is correct.
Desiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 20 students at her school and records their caffeine intake (mg) and the number of hours spent studying. What is the equation for the LSRL?
Caffeine = 2.544 + 0.164(hours)
Hours = 2.544 + 0.164(Caffeine)
Caffeine = 0.164 + 2.544(hours)
Hours = 0.164 + 2.544(Caffeine)
y= 40x+100, where x is number of weeks and y is weight in grams.
What does the y-intercept mean in context of the problem?
What type of correlation best describes the scatter plot shown?
positive, weak
positive, strong
negative, weak
no correlation
Estimate the correlation coefficient for this scatterplot.
r = 1.2
r = 0.89
r = 0
r = -0.89
The scatter plot shows the number coffee shops in different cities and the number of violent crimes. Which of the following is NOT true?
A) As the number of coffee shops increase, violent crimes appears to increase.
B) The line of best fit (regression line) shows a positive correlation
C) The data has a positive correlation coefficient
D) An increase in coffee shops causes an increase in violent crimes
If the correlation coefficient is r = 0.3, what type of data is shown?
Strong positive
Weak positive
Strong negative
Weak negative
When calculating the linear model (which is the equation for the Line of Best Fit for a set of quantitative data) our goal is to...
Minimize the residuals
Maximize the residuals
Ignore the residuals
What are residuals?
I predicted someone would score a 78% on their test, but they actually scored an 81%. What's the residual?
81 - 78 = 3
78 - 81 = -3
What's residual?
(a) is the use of a regression line for prediction outside the interval of x values used to obtain the line.
The ___________________ measures the percent of the variability in the response variable that is accounted for by the least-squares regression line.
coefficient of determination
x2
r2
coefficient of relaxation
Which of the following definitions are true...
Points with high leverage in regression have much larger or much smaller x values than the other points in the data set.
An outlier in regression is a point that does not follow the pattern of the data and has a large residual.
An influential point in regression is any point that, if removed, substantially changes the slope, y intercept, correlation, coefficient of determination, or standard deviation of the residuals.
All of the above
Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are provided. Notice that the horizontal axis on the residual plot is labeled “Fitted value,” which means the same thing as “predicted value. What was the actual activity level rating for the fish at a temperature of 20°C?
87
84
81
66
3
Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are provided. Notice that the horizontal axis on the residual plot is labeled “Fitted value,” which means the same thing as “predicted value. Which of the following gives a correct interpretation of s in this setting?
For every 1°C increase in temperature, fish activity is predicted to increase by 4.785 units.
The typical distance of the temperature readings from their mean is about 4.785°C.
The typical distance of the activity level ratings from the least-squares line is about 4.785 units.
The typical distance of the activity level readings from their mean is about 4.785 units.
At a temperature of 0°C, this model predicts an activity level of 4.785 units.
The following regression is for the relationship between the length (cm) and weight (g) of a small marine fish. Which of the following is the closest predicted weight of a fish that was 12 cm long according to this model?
2.63 g
3.50 g
13.89 g
33.23 g
426.58 g
This is a computer regression analysis of the relationship between log(Number of Employees at Microsoft) and year. Which of the following is the correct regression equation from this analysis if y=number of employees at Microsoft and x=year?
ŷ = -449.71 + .228x
logŷ = -449.71 + .228x
ŷ = -449.71 + .228(logx)
logŷ = .228 - 449.71x
ŷ = .228 - 449.71(logx)
A
B
C
D
E
A
B
C
D
E
This is what type of sample?
cluster
convenience
systematic
stratified
Chosen at random, 580 customers at a car dealership are contacted and asked their opinions of the service they received.
This is what type of sample?
convenience
stratified
simple random sample
cluster
A teacher wants to know the average time spent doing homework by the students in her class of 20 girls and 5 boys, so she randomly selects five students from the class to survey, paying no attention to their gender.
This is a form of:
Cluster Sampling
Systematic Sampling
Stratified Sampling
Simple Random Sampling
A poll about favorite sports is taken from 100 seniors in a high school where the senior class has 575 students. 23% of respondents said that baseball was their favorite sport.
The "100" is the ______
Sample Size
Population Size
Statistic
Parameter
A _______ is a subset of individuals in the population from which we actually collect data.
experiment
sample
population
survey
A sample should be
representative of only middle school students only
a very large group
representative of the population
representative of people who volunteer
A sample of students will be selected from all the students at a high school. Which of the following sampling methods is least likely to produce a representative sample of the students?
From a list of all student names, randomly select 50 names from the list for the sample.
Randomly choose five classrooms in the school and use all the students in those classrooms for the sample.
Divide the students into the four class years (freshman, sophomore, junior, senior) and randomly select students from each year in proportion to the number of students in each year.
From a numbered list of all student names, randomly choose a starting point and then choose every tenth student on the list.
From a randomly chosen home basketball game, choose every tenth student who enters the gymnasium.
A random number generator is used to select 12 students from a large statistics class to rate a statistics video. The 12 students selected are
the population.
a simple random sample of the class.
a convenience sample.
a voluntary response sample
Identify the sampling technique used: Corn is planted on a 200-acre field. The field is divided into 10-acre subplots. A sample of plants is taken from each subplot to estimate the harvest.
Simple Random
Stratified
Cluster
Systematic
A survey of 976 American households found that 32% of the households own two cars. Identify the the sample. {hint: a survey of what __)
All American households
976 American households
32% of Americans own two cars
two cars
Disneyland often surveys its guests as they exit a restaurant during their visit. The surveyor stands at the restaurant exit, counts the number of people leaving, and surveys every 25th guest.
This is a form of:
Simple Random Sample
Stratified Random Sample
Voluntary Response
Systematic Random Sampling
An independent research company wants to go door to door to survey people in the city of Fontana. The company decides to number all blocks within the city limit, randomly choose 1 block and survey all households on that block. This is an example of:
Simple Random Sample
Stratified Random Sample
Cluster Random Sample
Systematic Random Sampling
Identify the sampling design: The LFCC registrar wants to investigate attitudes of their graduates. The registrar randomly selects 100 names from each of the four past graduating classes.
cluster
volunteer
stratified
simple random
Identify the sampling technique used: Questioning students as they left school, a researcher asked 123 students about how they felt about the coming hurricane.
Simple Random
Stratified
Cluster
Convience
A teacher wants to know how well her students are doing on a topic. She randomly picks one class to survey.
Simple Random
Cluster
Stratified
Systematic
Which of the following doesn’t result in some form of bias?
Choosing AP students to survey regarding their GPA in order to estimate the average GPA in a school.
Polling a group of potential voters outside a Republican campaign office in order to estimate the proportion of city residents who favor a particular candidate.
Surveying people who work in the marketing department of a large corporation in order to assess employee satisfaction with management policies.
Choosing a stratified random sample of juniors and seniors at a high school in order to estimate the proportion of juniors and seniors who plan to go on to college.
Asking shoppers leaving a grocery store if they think groceries should cost less in order to estimate the proportion of city residents who think groceries cost too much.
A group of lobbyists has a list of 100 senators. They decide to talk to every 7th senator on the list about their position on farm subsidies.
Convenience
Systematic
Stratified
Simple Random
A teacher hands out an index card and asks ALL of her students to write down the following information: age, height (in inches), and what grade they are in.
Which of the following best describes her method of data collection?
Census
Simple Random Sample
Cluster Random Sample
Stratified Random Sample
State the type of sample. In order to determine the average IQ of ninth-grade students, a school psychologist obtains a list of all schools in the local public school system. She randomly selects five of these schools and administers an IQ test to all ninth-grade students at the selected schools.
Stratified Random Sample
Cluster Sample
SRS
Random Sample
Select the best answer: Every 100th hamburger manufactured is checked to determine its fat content.
random
systematic
stratified
cluster
What is the role of replication in experimental design?
Replication involves repeating an experiment multiple times to ensure that the results are consistent and reliable.
Replication is the process of collecting data from a single experiment to draw conclusions.
Replication refers to the use of different methods to analyze the same data set.
Replication is the act of sharing experimental results with other researchers.
What is a matched pairs design?
A design where subjects are randomly assigned to treatments.
A design where subjects are paired based on a certain characteristic, and each pair is assigned to different treatments.
A design that involves only one group of subjects receiving multiple treatments.
A design that compares two independent groups without pairing.
What is the significance of sample size in an experiment?
Larger sample sizes generally lead to more reliable results and reduce variability.
Smaller sample sizes are always preferred for quicker results.
Sample size has no impact on the reliability of results.
Sample size only affects the cost of the experiment.
What is the difference between a treatment group and a control group?
A treatment group receives the treatment being tested, while a control group does not receive the treatment and serves as a baseline for comparison.
A treatment group is larger than a control group and includes more participants.
A control group receives the treatment being tested, while a treatment group does not receive any treatment.
Both groups receive the same treatment but are monitored differently.
What is the importance of a control group in an experiment?
A control group is important because it provides a baseline to compare the effects of the treatment, helping to isolate the treatment's impact.
A control group is used to ensure that the experiment is conducted in a controlled environment without any variables.
A control group is necessary to increase the sample size of the experiment and improve the reliability of the results.
A control group helps to eliminate the need for randomization in the selection of participants.
What is a response variable?
A variable that is manipulated in an experiment.
The outcome that is measured in an experiment to assess the effect of the treatment.
A variable that remains constant throughout the experiment.
A factor that influences the response variable.
What is bias in the context of experimental design?
A systematic error that can lead to incorrect conclusions in an experiment.
A random variation that affects the results of an experiment.
A method to ensure that all variables are controlled during an experiment.
A technique used to increase the sample size in an experiment.
What is a blocking design?
A method of random assignment without grouping subjects.
An experimental design that involves dividing subjects into groups based on a certain characteristic before random assignment to treatment groups.
A technique used to eliminate bias in observational studies.
A design that focuses solely on the outcome of a single treatment.
What is undercoverage in sampling?
Undercoverage occurs when some members of the population are inadequately represented in the sample.
Undercoverage is when the sample size is too large for the population.
Undercoverage happens when all members of the population are included in the sample.
Undercoverage refers to the overrepresentation of certain groups in the sample.
What is an observational study?
A type of study where researchers impose treatments on subjects.
A type of study where researchers observe subjects without imposing treatments.
A type of study that only involves surveys and questionnaires.
A type of study that requires laboratory experiments.
Define confounding in experimental design.
Confounding occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.
Confounding is the process of randomly assigning subjects to different treatment groups.
Confounding refers to the situation where a variable is manipulated to observe its effect on another variable.
Confounding happens when the sample size is too small to draw valid conclusions.
What is the difference between qualitative and quantitative data?
Qualitative data consists of numerical values that can be measured, while quantitative data describes characteristics or qualities.
Qualitative data describes characteristics or qualities, while quantitative data consists of numerical values that can be measured.
Qualitative data is always more reliable than quantitative data.
Quantitative data is subjective, while qualitative data is objective.
What is an experiment in the context of experimental design?
A study that involves random sampling of subjects to gather data.
A study in which treatments are imposed on subjects to observe the effects on a response variable.
A method of collecting qualitative data through interviews and surveys.
A process of analyzing existing data to find patterns and correlations.
What is the purpose of randomization in an experiment?
To ensure that all participants receive the same treatment.
To make the treatment groups as similar as possible, reducing bias and confounding.
To increase the sample size for better statistical power.
To allow researchers to manipulate variables more easily.
What is a completely randomized design?
A design where treatments are assigned based on the researcher's preference.
A design where treatments are assigned to all experimental units completely by chance.
A design that requires a specific order of treatment application.
A design that uses a fixed number of experimental units for each treatment.
The probability that a randomly chosen American is a Republican is 0.35. What is the probability that in a sample of 10 Americans, that at least 1 will be a Republican?
0.9865
0.2275
0.0725
0.0135
Pepsi is running a sales promotion in which 12% of all bottles have a "FREE" logo under the cap. If you buy a 6-pack of bottles, what is the probability that you will find at least 1 "FREE" logo?
.464
.536
.12
0
What is the complement of choosing a red marble if there are 8 red marbles in a jar of 15?
P' = 3/15
P' = 7/15
P' = 8/15
P' = 15/8
In an AP Statistics class, 57% of students eat breakfast in the morning, 80% of them floss their teeth, and 46% of the students do both. What is the probability that a randomly chosen student eats breakfast but does not floss their teeth?
9%
11%
34%
91%
In an AP Statistics class, 57% of students eat breakfast in the morning, 80% of them floss their teeth, and 46% of the students do both. What is the probability that a randomly chosen student eats breakfast or flosses their teeth?
91%
9%
11%
34%
The probability of a tourist visiting an area cave is .7, and of a tourist visiting a nearby park is .6. The probability of visiting both places on the same day is .4. The probability that a tourist visits at least one of these two places is:
.08
.28
.42
.9
Five juniors and four seniors have applied for two open student council positions, and administrators have decided to pick two new members randomly. What is the probability that they are both from the same grade?
.395
.444
.506
.569
A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads on the next flip is:
greater than 50%, it's due to happen.
50%
less than 50%, since tails is happening so much.
Can't be determined
According to the National Telecommunication and Information Administration, 50.5% of U.S. households had internet access in 2001. What is the probability that four randomly selected U.S. all had internet access in 2001?
6.5%
12.6%
49.5%
50.5%
Pepsi is running a sales promotion in which 12% of all bottles have a "FREE" logo under the cap. If you buy a 6-pack of bottles, what is the probability that you will find at least 1 "FREE" logo?
.464
.536
.12
0
A bicycle shop equips 60% of its bikes with a water bottle holder, and 55% of its bikes are equipped with a kick stand. 34% of the bikes have both features. What is the probability that a randomly chosen bike has a kick stand GIVEN THAT it has a water bottle holder?
34%
56.7%
61.8%
81%
100 people were surveyed. 54 were female, and 46 were male. 33 of the females said they were democrats, and 30 of the males said they were republicans. If a person is randomly selected, what is the probability that its a democrat?
49%
46%
54%
51%
100 people were surveyed. 54 were female, and 46 were male. 33 of the females said they were democrats, and 30 of the males said they were republicans. If a person is randomly selected, what is the probability that its a democrat GIVEN THAT it is a female?
.67
.49
.61
.33
100 people were surveyed. 54 were female, and 46 were male. 33 of the females said they were democrats, and 30 of the males said they were republicans. If two people are randomly selected, what is the probability they are both males?
.30
.46
.25
.21
100 people were surveyed. 54 were female, and 46 were male. 33 of the females said they were democrats, and 30 of the males said they were republicans. If a person is randomly selected, what is the probability a male is chosen GIVEN THAT its a republican?
.59
.65
.35
.41
If P(A) = 0.4 and P(B) = 0.3, what is P(A or B) using the general addition rule?
0.7
1.0
0.5
0.2
Data were collected on the ages, in years, of the men and women enrolled in a large sociology course. Let the random variables M and W represent the ages of the men and women, respectively. The distribution of M has mean 20.7 years and standard deviation 1.73 years. The distribution of W has mean 20.2 years and standard deviation 1.60 years. Of all of those enrolled in the course, 54 percent are men and 46 percent are women. What is the mean age of the combined distribution of both men and women in the course?
20.2 years
20.43 years
20.45 years
20.47 years
20.50 years
The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W=7+2X. What are the mean and standard deviation of W?
The mean is 24, and the standard deviation is 6.
The mean is 24, and the standard deviation is 13.
The mean is 31, and the standard deviation is 3.
The mean is 31, and the standard deviation is 6.
The mean is 31, and the standard deviation is 13.
The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S has mean 7 and standard deviation 3. If R and S are independent, what are the mean and standard deviation of the distribution of R − S?
Mean 3 and standard deviation 1
Mean 3 and standard deviation 5
Mean 3 and standard deviation 7
Mean 17 and standard deviation 1
Mean 17 and standard deviation 5
The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S has mean 7 and standard deviation 3. If R and S are independent, what are the mean and standard deviation of the distribution of R + S?
Mean 3 and standard deviation 1
Mean 3 and standard deviation 5
Mean 3 and standard deviation 7
Mean 17 and standard deviation 1
Mean 17 and standard deviation 5
Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. If the customer rolls the dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer would expect to pay for these second movies?
$0.45
$0.47
$0.67
$3.00
$9.40
A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second box contains 8 tags, numbered 20 through 27, with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags?
13.5
14.5
15.0
27.0
29.0
Let X represent the number on the face that lands up when a fair six-sided number cube is tossed. The expected value of X is 3.5, and the standard deviation of X is approximately 1.708. Two fair six-sided number cubes will be tossed, and the numbers appearing on the faces that land up will be added. Which of the following values is closest to the standard deviation of the resulting sum?
1.708
1.848
2.415
3.416
5.835
A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X - Y ?
17.49
24.0
12.51
20.38
6.0
The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y ?
The mean is 20 and the standard deviation is 102.
The mean is 20 and the standard deviation is 50.
The mean is 22 and the standard deviation is 102.
The mean is 22 and the standard deviation is 100.
The mean is 22 and the standard deviation is 50.
A company sells concrete in batches of 5 cubic yards. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?
$332.00
$432.00
$532.00
$1,343.75
$1,400.00
A friend has placed a large number of plastic disks in a hat and invited you to select one at random. He informs you that half are red and half are blue. If you draw a disk, record the color, replace it, and repeat 100 times, which of the following is true?
It is unlikely you will choose red more than 50 times.
If you draw 10 blue disks in a row, it is more likely you will draw a red on the next try.
The overall proportion of red disks drawn should be close to 0.50.
The chance that the 100th draw will be red depends on the results of the first 99 draws.
Joe reads that 1 our of 4 eggs contains salmonella bacteria. So he never uses more than 3 eggs in cooking. If eggs do or don't contain salmonella independently of each other, the number of contaminated eggs when Joe uses 3 chosen at random has the following distribution:
Binomial; n = 4 and p = 1/4
Binomial; n = 3 and p = 1/4
Binomial; n = 3 and p = 1/3
Geometric; p = 1/4
Geometric; p = 1/3
A binomial event has n = 60 trials. The probability of success on each trial is 0.4. Let X be the count of successes of the event during the 60 trials. What are mean X and standard deviation X?
24; 3.79
24; 14.4
4.9; 3.79
4.9; 14.4
The probability that an American household will have at most 3 cars is...
0.93
0.20
0.13
0.07
The probability that an American household will have at least 2 cars is...
0.55
0.35
0.45
0.93
What's the expected number of cars in a randomly selected American household?
1.00
1.75
1.84
2.00
How would you interpret the expected value in number 3?
The maximum number of cars for the household is Exp(C).
The average number of cars for the household is Exp(C).
If we randomly select many households, the average number of cars per household will be approximately by Exp(C).
If we randomly select many households, the average number of cars per household will vary approximately by Exp(C).
A deck of cards contains 52 cards , of which 4 are aces. You are offered the following wager: Draw one card at random from the deck. You win $10 if the card drawn is an ace. Otherwise, you lose $1. If you make this wager very many times, what will be the mean amount you win?
About -$1, because you will lose most of the time.
About $9, because you win $10 but lose only $1.
About -$0.15; that is, on average you lose about 15 cents.
About $0.77; that is, on average you win about 77 cents.
About $0, because the random draw gives you a fair bet.
A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?
Mean Y = $1.50 and St. Dev Y = $22.50
Mean Y = $1.50 and St. Dev Y = $33.75
Mean Y = $75 and St. Dev Y = $18.37
Mean Y = $75 and St. Dev Y = $22.50
Mean Y = $75 and St. Dev Y = $33.75
Seventeen people have been exposed to a particular disease. Each one independently has 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital's capacity will be exceeded?
0.011
0.035
0.092
0.965
A test for extrasensory perception (ESP) involves asking a person to tell which of 5 shapes - a circle, star, triangle, diamond, or heart - appears on a hidden computer screen. On each trial, the computer is equally likely to select any of the 5 shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first 4 shapes incorrectly but gets the 5th correct?
(4/5)4
(4/5)4 * (1/5)
(5/1) * (4/5)4 * (1/5)
A fast-food restaurant runs a promotion in which certain food items come with game pieces. According to the restaurant, 1 in 4 game pieces is a winner. If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 price?
The probability of x, the number of tires needing replacement on a randomly selected automobile checked at a certain inspection station is given in the following table. What is the standard deviation of X?
1.2
2.52
1.58
