WorksheetsStatistical Modeling SLO Pretest
Total questions: 60
Worksheet time: 3hrs 34mins
Which of the following is an example of a quantitative variable?
Supervising Manager
Hours Worked
Pay Scale Group
Certification
Because the long-term benefit of Covid vaccines have not been determined, medical researchers investigated the health histories of the past year of 120 recipients who were diagnosed with Covid within one year after being vaccinated. They asked questions to determine length of illness, severity of illness, and number of times they had contracted the disease. Identify the population in the study.
Numbers Who Became Severely Ill from Covid
Persons Who Have Been Vaccinated
Persons Who Became Ill with Covid
120 vaccinated individuals who contracted Covid
{5, 8, 6, 5, 4, 9, 8, 7, 6, 3, 8, 7, 5, 6, 7, 8}
What is the interquartile range of the data?
Administrators at Riverview High School surveyed a random sample of 100 of their seniors to see how seniors at the school felt about the lunch offering at the school's cafeteria.
The population is all high school seniors in the world; the sample is all of the seniors at Riverview High.
The population is all students at Riverview High; the sample is all of the seniors at Riverview High.
The population is all seniors at Riverview High; the sample is the 100 seniors surveyed.
One group of subjects was given an herbal supplement and another group was given a placebo. After one year, the number of illnesses each group had was compared.
Observational Study
Experiment
Which of the following is a key distinction between well designed experiments and observational studies?
More subjects are available for experiments than for observational studies.
Ethical constraints prevent large-scale observational studies.
Experiments are less costly to conduct than observational studies.
An experiment can show a direct cause-and-effect relationship, whereas an observational study cannot.
Tests of significance cannot be used on data collected from an observational study.
I want to estimate the proportion of all adults in Chula Vista who graduated from high school. I select a random sample of addresses and go to those houses. When an adult answers the door, I ask if they had graduated from high school. If a child answers the door, I ask for an adult. If there is none there at the time, I return at another time to complete the survey. What is the most prominent bias?
Non-response bias
Response bias
Voluntary response bias
Undercoverage
What is the relative frequency of teachers who live in Harlem?
4%
12%
16%
25%
The heights, in inches, of eight football players are given below.
76, 70, 72, 70, 69, 71, 78, 74
Which box plot represents these data?
Which has a greater interquartile range?
Airplane A
Airplane B
Both the same
Describe the shape of the distribution.
skewed to the left
skewed to the right
roughly symmetric
uniform
Which measures of center and variability should be used to describe the distribution?
mean and standard deviation
mean and IQR
median and standard deviation
median and IQR
Which calculations would you use to check for outliers?
Check all that apply.
Q1 - 1.5(IQR)
Q1 + 1.5(IQR)
Q3 - 1.5(IQR)
Q3 + 1.5(IQR)
What is the relationship between the mean and the median?
mean < median
mean > median
mean = median
If I tell you that you scored at the 55th percentile on your final exam, you would know:
55% of the class scored the same or worse than you did
You earned a 55% on the exam
You failed the exam
45% of the class scored worse than you did
Given the data set: 1, 2, 3, 6, 9, 11, 45, 102, calculate the percentile for the data value 11 in this set.
70th percentile
62.5th percentile
72.5th percentile
75th percentile
According to the empirical rule, how much of the data falls within 2 standard deviations of the mean?
25%
68%
95%
99.7%
Joanne's score on a test gives her a Z-score is -1.50. What does this mean?
Joanne didn't take the test yet.
Joanne's test score is 1.50 standard deviations below the average test score.
Joanne did better than 1.50 times her peers.
Joanne's test score, on average, was 1.5 points lower than the other test scores.
If Gonzalo's score is 87, the class mean is 82, and the s = 4, what is Gonzalo's z-score?
The mean test score for a class was 76 with a standard deviation of 5 points, and the shape was skewed left. The teacher decides to add 4 points to every students test score. What is the new mean, standard deviation, and shape for the distribution of test scores?
mean=80, SD=5, shape is skewed left
mean=80, SD=9, shape is skewed left
mean=80, SD=5, shape is more skewed left
mean=80, SD=9, shape is approx. symmetric
A 50 point test had a mean of 42 with a standard deviation of 5 points. The original shape of the distribution of test scores was approximately symmetric. The teacher decides to multiply all scores by 2 (so the total is out of 100). What is the new mean, standard deviation and shape for the distribution of test scores?
mean=84, SD=10, approx. symmetric
mean=84, SD=5, approx. symmetric
mean=42, SD=5, approx. symmetric
mean=84, SD=10, slightly skewed right
The wait time at your local McDonald's varies according to a normal distribution, with a mean of 7 minutes and standard deviation of 1.35 minutes. Approximately what proportion of their wait times are over 9 minutes?
0.033
0.069
0.189
0.191
Mrs. G's newborn baby girl sleeps for approximately 20.1 hours per day. Newborn sleep schedules are normally distributed with a standard deviation of 0.8 hours. If you know Mrs. G's daughter is at the 67th percentile for sleep, what is the mean sleep time of all newborn baby girls?
19.75 hours
19.98 hours
20.45 hours
18.45 hours
Which of the following correlation coefficients best correspond with the scatterplot?
1
-0.7
0
-0.1
Interpret the correlation of r = -0.9
strong and positive
strong and negative
weak and positive
weak and negative
A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.
y = 12 + 1.5x
y = 12 - 1.5x
y = 0.67x - 8
y = -8 + 0.67x
What happens to the variability of a sampling distribution as n(sample size) increases?
It increases.
It decreases.
It stays the same.
The Gallup Poll asked a random sample of 240 adults if they had a speeding violation. 96 said they did. Let p-hat be the proportion of people in the sample who had speeding tickets. The local police department reports that 42% of the citizens had speeding tickets. Suppose this claim is true. What is the mean of the sampling distribution?
0.4
0.42
0.58
0.6
mean of sample proportion
standard deviation
If a population is normally distributed with a mean of 60 and a standard deviation of 5, what can we say about the shape of the sampling distribution of the sample mean for a sample size of 30?
Uniformly distributed
Negatively skewed
Positively skewed
Normally distributed
If a population is normally distributed with a mean of 60 and a standard deviation of 5, what are the mean and standard deviation of the sampling distribution of the sample mean for a sample size of 30?
μx̄ = 60; σx̄ = 30
μx̄ = 30; σx̄ = 15
μx̄ = 60; σx̄ = 0.167
μx̄ = 60; σx̄ = 0.913
78% of flights on major airlines arrive on time. A random sample was taken of 100 flights.
Find the probability that more than 70% of the 100 randomly selected flights are on time.
0.5077
0.0267
0.9999
0.9733
Interpret the following confidence interval.
10<μ<30
We are 95% confident the true population mean lies between 10 and 30.
There is a 95% chance the true population mean lies between 10 and 30.
95% of samples will have a mean between 10 and 30.
The true population mean lies between 10 and 30 95% of the time.
A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the Internet?
0.321 < p < 0.379
0.316 < p < 0.384
0.309 < p < 0.391
0.305 < p < 0.395
Suppose that a confidence interval for hours worked by students was computed to be (8.82, 10.78). Which of these is a valid interpretation of this confidence interval?
There is a 95% probability that the average number of hours worked by all students is between 8.82 and 10.78 hours.
There is a 95% probability that a randomly selected student worked between 8.82 and 10.78 hours.
We are 95% confident that the population average number of hours worked by all students is between 8.82 and 10.78 hours.
We are 95% confident that the average number of hours worked by the students in our sample is between 8.82 and 10.78 hours.
Thirty randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 99 percent confidence interval for the mean score of all students from which the sample was gathered.
89.08 < μ < 94.92
87.27 < μ < 96.73
87.29 < μ < 96.71
87.77 < μ < 96.23
A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properly, a random sample of 50 bottles was selected and the mean number of ounces for the 50 bottles was computed. A test of the hypotheses H0 : µ = 12 versus Ha: µ < 12 was conducted, where µ represents the population mean number of ounces of the beverage dispensed per bottle by the machine. The p-value for the test was 0.08. Which of the following is the most appropriate conclusion to draw at the significance level of α = 0.05?
Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.
Because the p-value is greater than the significance level, there is not convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.
Because the p-value is less than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.
Eight percent of the bottles will be filled with less than 12 ounces.
A Gallup poll report revealed that 72% of teens said they rarely or never argue with their friends. Yvonne wonders if this result is true for her school. She surveys a random sample of 150 students and 64% of them say they rarely or never argue with friends. She uses the data to perform a test of Ho: p = 0.72 versus Ha: p=/= 0.72.
The test yields a p-value of 0.0291. What conclusion would you make for a significance level of 5%?
Since our p-value of 0.0291 is more than 5%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.
Since our p-value of 0.0291 is less than 5%. we fail to reject the null hypothesis. We do not have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.
Since our p-value of 0.0291 is more than 5%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.
Since our p-value of 0.0291 is less than 5%. we reject the null hypothesis. We have convincing evidence that the proportion of teens in her school who rarely or never argue with their friends is different from 0.72.
Resting pulse rate is an important measure of the fitness of a person's cardiovascular system, with a lower rate indicative of greater fitness. The mean pulse rate for all adult males is approximately 72 beats per minute. A random sample of 25 male students currently enrolled in the Agriculture School at a major university was selected and the mean resting pulse rate was found to be 80 beats per minute with a standard deviation of 20 beats per minute. The experimenter wishes to test if the students are less fit, on average, than the general population. The null and alternative hypotheses are:
H0: μ = 72; Ha: μ < 72
H0: x-bar = 72; Ha: x-bar < 72
H0: μ = 80; Ha: μ =72
H0: x-bar = 80; Ha: x-bar > 72
H0: μ = 72; Ha: μ > 72
Lumber companies dry freshly cut wood in kilns before selling it. A certain percentage of boards develop cracks on their ends during drying. The current drying procedure is known to produce cracks in 16% of boards. The drying supervisor wants to try a new method that she believes will result in a proportion of cracked boards that is less than 16%.
Write the appropriate hypotheses.
Ho: p = 0.16
Ha: p = 0.16
Ho: p = 0.16
Ha: p =/= 0.16
Ho: p = 0.16
Ha: p > 0.16
Ho: p = 0.16
Ha: p < 0.16
In a recent survey of 1503 adults in the United States, 53% said they use both a landline and a cell phone. the 53% is a...
parameter
statistic
The median home value of all homes in Ohio is $138,200. The median home values for a sample of 100 homes taken was $139,500. The value of $138,200 is a
statistic
parameter
Assuming the null hypothesis is true, which tells "the probability of obtaining a result we got?"
T - Value
P - Value
Significance Level
Mean
Alternate Hypothesis
What does it mean when a test is statistically significant?
It is merely due to chance.
The p-value is large.
The result is UNLIKELY due to chance.
it is important in practical terms
