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WorksheetsFull Semester 2 Review
Total questions: 140
Worksheet time: 7hrs 7mins
Which of the following best describes a Type I error?
The null is true, but we mistakenly reject it.
The null is false and we reject it.
The null is false, but we fail to reject it.
The null is true but we fail to reject it.
The null is true, and we fail to reject it.
Which of the following best describes a type II error?
The null is true, but we mistakenly reject it.
The null is false and we reject it.
The null is false, but we fail to reject it.
The null is true but we fail to reject it.
Te null is false, and we reject it.
For a class project, a student in a statistics class surveys the monthly rent for 32 unfurnished one-bedroom apartments in Boston and finds the mean monthly rent to be $1400 with a standard deviation of $220.
Find the margin of error for the sample mean. (assuming 95% confidence) Round to the nearest hundredth
$77.78
$4.31
$188.78
$494.97
For a class project, a student in a statistics class surveys the monthly rent for 32 unfurnished one-bedroom apartments in Boston and finds the mean monthly rent to be $1400 with a standard deviation of $220.
Find the 95% confidence interval for the population mean Round to the nearest hundredth
[1322.22, 1477.78]
[1395.69, 1404.31]
[1211.22, 1588.78]
[905.03, 1894.97]
A random sample of 45 life insurance policy holders showed that the average premiums paid on their life insurance policies was $340 per year with a standard deviation of $62. Construct a 95% confidence interval for the population mean. Round to the nearest hundredth
[321.52, 358.48]
[238.63, 441.37]
[253.64, 426.36]
[328.57, 351.43]
Complete the following statement about the change in size.
If you increase the size of your sample, the ME will . . . .
increase
decrease
stay the same
Complete the following statement about the change in size.
If your sample has a larger mean, the ME will . . . .
increase
decrease
stay the same
Complete the following statement about the change in size.
If your sample has a larger standard deviation, the ME will . . . .
increase
decrease
stay the same
What does a 95% confidence level mean in the context of constructing a confidence interval?
There is a 95% chance the sample data is correct.
95% of the sample data lies within the interval.
We are 95% confident that the interval (in context) contains the population parameter.
We are 95% confident that the sample parameter estimates the population statistic.
What is the effect of increasing the confidence level on the width of the confidence interval?
It decreases the width of the confidence interval.
It increases the width of the confidence interval.
It has no effect on the width of the confidence interval.
It first increases then decreases the width of the confidence interval.
How does decreasing the standard deviation of the sample data affect the margin of error in a confidence interval?
It increases the margin of error.
It decreases the margin of error.
It has no effect on the margin of error.
It first decreases then increases the margin of error.
For a 99% confidence interval, which of the following z∗ values is most appropriate?
1.64
1.96
2.33
2.58
A Census Bureau report on the income of Americans says that with 90% confidence the mean income of all US households in a recent year was $57,005 with a margin of error of $742. This means that
90% of all households had incomes in the range $57,005 + $742
we can be sure that the median income for all households in the country lies in the range $57,005 + $742
90% of the households in the sample interviewed by the Census Bureau had incomes in the range $57,005 + $742
the Census Bureau got the result $57,005 + $742 using a method that will cover the true median income 90% of the time when used repeatedly
90% of all possible samples of this same size would result in a sample median that falls within $742 of $57,005
You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of t* you would use for this interval is
1.645
1.699
1.697
1.96
2.045
The weights (in pounds) of three adult males are 160, 215, and 195. The standard error of the mean of these three weights is
190
27.84
22.73
16.07
13.13
A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content σ ?
90% confidence; n = 25
90% confidence; n = 50
95% confidence; n =25
95% confidence; n =50
n=100 at any confidence level
One reason for using a t distribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that
z can be used only for large samples
z requires that you know the population standard deviation
σz requires that you can regard your data as an SRS from the population
z requires that the sample size is at most
a z critical value will lead to a wider interval than a t critical value.
A teacher is interested in performing a hypothesis test to compare the mean math score of the girls and the mean math score of the boys. She randomly selects 10 girls from the class and then randomly selects 10 boys. She arranges the girls' names alphabetically and uses this list to assign each girl a number between 1 and 10. She does the same thing for the boys.
1-sample t-test. The teacher should compare the sample mean for the girls against the population mean for the boys.
Paired t-test. Since the boys and girls are in the same class, and are hence dependent samples, they can be linked.
Either two-sample or paired t-test will work.
Two-sample t-test. There is no natural pairing between the two populations.
Paired t-test. Since there are 10 boys and 10 girls, we can link the two samples.
A high school coach uses a new technique in training middle distance runners. He records the times for 4 different athletes to run 800 meters before and after this training. A 90% confidence interval for the difference of the means before and after the training, μB - μA, was determined to be (2.6, 4.8).
We know that 90% of all random samples done on runners at this high school will show that the mean time difference before and after the training is between 2.6 and 4.8 seconds.
There is a 90% probability that a randomly selected middle distance runner at this high school will have a time for the 800-meter run that is between 2.6 and 4.8 seconds shorter after the training than before the training.
Based on this sample, with 90% confidence, the average time for the 800-meter run for middle distance runners at this high school is between 2.6 and 4.8 seconds shorter after the new training.
We know that 90% of the middle distance runners shortened their times between 2.6 and 4.8 seconds after the training.
Based on this sample, with 90% confidence, the average time for the 800-meter run for middle distance runners at this high school is between 2.6 and 4.8 seconds longer after the new training.
Five students took a math test before and after tutoring. Their scores were as follows. Do the data suggest that there is a difference in the math scores? Perform a paired t-test at the 5% significance level.
No, the data does not provide sufficient evidence to conclude that the tutoring has an effect on the math scores.
Yes, the data does provide sufficient evidence to conclude that the tutoring has an effect on the math scores.
What is the alternative hypothesis ( Ha ) in hypothesis testing?
The hypothesis that there is no significant effect or difference
The hypothesis that there is a significant effect or difference
The hypothesis that the sample mean is equal to the population mean
The hypothesis that the sample mean is greater than the population mean only
What role does the significance level play in hypothesis testing?
It determines the sample size needed for the test
It is the threshold for deciding whether to reject the null hypothesis
It calculates the test statistic
It increases the accuracy of the test
Choose the statistical question from the options below.
What is the speed of light?
How many pages does the longest book in your library have?
What is the average amount of time students spend on social media each day?
Who was the first person to climb Mount Everest?
ANOVA testing is used for ...
Test for one mean
Test for two means
Test for three or more means
Test for independence between two variables
A large sample F-ratio (F test statistic) is likely to lead us to ____ in an ANOVA test.
reject Ho
not reject Ho
reject Ha
not reject Ha
Identify the appropriate statistical test to see if there is a difference in the mean salaries.
t-test for one mean
t-test for two means
chi-square test of independence of two variables
F-test for an ANOVA
Formulate the alternative hypothesis.
μ1 & μ2 are not the same
μ2 & μ3 are not the same
μ1 = μ2 = μ3
At least one mean is different
Compute the F-ratio (test statistic) when MSB = 391.2 and MSW = 174.1714
391.2
3.4668
2.246
0.1306
Compute the F critical value for α =1%, N = 24 and k = 3
2.246
4.718
5.781
2.575
The correct decision is ...
reject Ho
fail to reject Ho
reject H1
fail to reject H1
The correct conclusion is ...
There are significant differences in mean salaries among the 3 majors.
There are no significant differences in mean salaries among the 3 majors.
We need to do a chi-square test to find the differences.
We need to do a Bonferroni test to find the differences.
The dfB = 4 and dfW = 20. What would be the total N for an ANOVA?
19
20
24
25
The following are assumptions for ANOVA except:
Variance must be homogenous
There should be 4 or more independent groups
Data must be normally distributed
Randomly selected
To determine whether the test statistic of ANOVA is statistically significant, it can be compared to a critical value. What two pieces of information are needed to determine the critical value?
sample size, number of groups
mean, sample standard deviation
expected frequency, obtained frequency
MSTR (Mean Square Treatment), MSE
The ANOVA procedure is a statistical approach for determining whether or not
The means of two or more samples are equal
the means of more than two samples are equal
the means of two or more populations are equal
the means of two samples are equal
ANOVA tests use which of the following distributions?
F
t
Z
Chi-square
The one-way ANOVA is used to test statistical hypotheses concerning which of the following?
Means
Proportions
Variances
Standard deviations
Which of the following is NOT an assumption for the ANOVA test?
Populations are normally, or approximately normally, distributed
Samples are dependent
Samples are random
Population variances must be equal
A student tests the reaction times of the same 20 students before or after drinking coffee. How should she analyse the data to see if coffee has had an effect?
Use a paired T-test
Use an independent T-test
Use an ANOVA
Draw a scatter graph and look for correlation
A student wants to test whether 3 activities (treadmill, cross trainer or rowing machine) have significantly different effects on the heart rate. How should they test the data?
Use a paired T-test
Use an independent T-test
Use an ANOVA
Draw a scatter graph and look for correlation
A student wants to test whether cats are more intelligent than dogs. How should he analyse his data?
Use a paired T-test
Use an independent T-test
Use an ANOVA
Draw a scatter graph and look for correlation
A student wants to know if the water lost by plants in transpiration is significantly different in 4 different environmental conditions. 20 plants were left in each of the 4 conditions and the water loss measured after 2 days. How should this data be analysed?
Use a paired T-test
Use an independent T-test
Use an ANOVA
Draw a scatter graph and look for correlation
A T-test is used to test for a difference in weight between mice fed on 2 different diets. The p-value calculated is 0.3, this means that:
The null hypothesis should fail to be rejected as p is greater than 0.05 : there is no significant difference between groups,
The null hypothesis should be rejected as p is greater than 0.05 : there is a significant difference between groups
There is a clear correlation between the diet and the size
The alternative hypothesis should be accepted as p is less than 5%
A T-test was used to test for a difference in blood pressure before and after drinking chicha morada. The p-value calculated is 0.01, this means that:
The null hypothesis should be accepted as p is greater than 0.05 : there is no significant difference between groups,
The null hypothesis should be rejected as p is less than 0.05 : there is a significant difference between groups
There is a clear correlation between the diet and the size
The alternative hypothesis should be rejected as p is less than 5%
A T-test was performed on some data. The p-value was 0.5 . The investigators should:
Fail to reject the null hypothesis
Reject the null hypothesis
Not enough information to say
The experiment is testing power differences between male and female. Do you think this will be a one-tailed or a two-tailed test?
One-tailed
Two-tailed
What are the degrees of for this set of data freedom?
(a)
What would be the degrees of freedom for this independent t test?
(a)
Which of the following sets of hypotheses can be used to test the following: Is
there a difference in the average time spent practicing for NBA and MLB
players?
Ho: μdiff = 0 and Ha: μdiff ≠ 0
Ho: μdiff ≠ 0 and Ha: μdiff = 0
Ho: μNBA = μMLB and Ha: μNBA ≠μMLB
Ho: μNBA ≠μMLB and Ha: μNBA = μMLB
What is the percentage of people that purchased no food?
What would you divide to find the relative frequencies by row? (Select all that apply.)
55/118
55/143
88/103
88/143
Which of the following is represented by the histogram?
Of the 20 riders represented in the graph, over 50% are 30 years of age or older.
One fourth of the riders represented in the graph are younger than 40 years old.
Half the riders represented in the graph are between the ages 10-29.
Six percent of the riders represented in the graph are between the ages 10 and 19.
True or False? Over 50% of the students watch between 5 and 14 hours of television on the weekend?
TRUE
FALSE
Are Democrats and Republicans equally likely to vote?
Paired T Test
Independent T Test
ANOVA
One Sample T Test
Is the average cost of a European vacation less than $8,000?
Independent T Test
Paired T Test
ANOVA
One Sample T Test
Is the starting salary of computer science, engineering, and science
majors the same after graduation?
Independent T Test
Paired T Test
ANOVA
Chi Square Goodness of Fit
Do peaches weigh more than 40g on average?
Independent T Test
Paired T Test
ANOVA
One Sample T Test
Does a person’s IQ score change after going through college?
Independent T Test
Paired T Test
ANOVA
One Sample T Test
Does blood pressure increase after going through a haunted house?
Independent T Test
Paired T Test
ANOVA
One Sample T Test
How many degrees of freedom will be present?
4
5
6
7
The shape of the Chi-Square distribution is ___.
Left Skewed
Right Skewed
Unimodal & Symmetric
Bimodal & Symmetric
How do you find degrees of freedom for a chi-square goodness of fit test?
one less than the sample size
one less than the population
total number divided 2
total number times 2
Aw, nuts! A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% brazil nuts. To test this claim, a quality-control inspector takes a random sample of 150 nuts from the latest batch. The one-way table below displays the sample data. What is the appropriate null hypothesis
U1-U2=U3=U4
Mixed nut proportions are proportioned the same as they claim
At least one of the four types in the population is different than expect
the observed counts are equally distributed
Python eggs How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the mother. Here are the data on the number of eggs that hatched and didn’t hatch.
If the p-value is .08 and you use .05 as your alpha, what is your conclusion
Fail to reject: We do not have sufficient evidence that distribution of hatched is different for water temperature options
Reject: We do not have sufficient evidence that distribution of hatched is different for water temperature options
Fail to reject: We do have sufficient evidence that distribution of hatched is different for water temperature options
If a chi-squared number is 5.29 with a df of 6, what is the p-value?
.38
.49
.51
What percent of students are satisfied with student government?
56%
62%
25%
21%
P(Plane | France)
0.25
0.3
0.17
0.08
In a 10x7 contingency table, what are the degrees of freedom?
70
69
54
45
Find the marginal distribution of the Military dependent status .
≈ 49%
≈ 3%
≈ 96%
≈ 51%
A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race of the driver. The results are summarized in the table provided. Assuming H0 is true, the expected number of Hispanic drivers who would receive a ticket is.....
(Hint: use expected number = np)
What is the
χ2 calculated value for the following situation.
6.65
6.66
0.00991
1
If we are testing at a 5% significance level and our p-value is 0.00453, what is the conclusion?
Accept Ho
Reject Ho
We need to know chi-squared
You cannot do this problem without a calculator
Find the chi-squared calculated value for the table.
0.486170447
1.442392006
1.45
2
Given that a student is male, what is the probability that maths is their favorite?
0.491
0.225
0.443
.508
For a p-value from the calculator of 1.32355E-3 what would the conclusion be if testing at 10% significance level?
Accept Ho
Reject H1
Reject Ho
Need to know the chi-squared number
All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High-frequency EM radiation is thought to be a cause of cancer. The lower frequencies associated with household current are generally assumed to be harmless. To investigate the relationship between current configuration and type of cancer, researchers visited the addresses of a random sample of children who had died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either a high-current configuration (HCC) or a low-current configuration (LCC). Computer software was used to analyze the data.
The χ2 statistic is equal to;
(give your answer to 3 decimal places
(a)
What percent of the respondents are juniors?
28%
18%
25%
94%
What percent of the respondents are satisfied and juniors?
62%
28%
68%
17%
What percent of the participants were given a placebo?
56%
44%
60%
40%
What percent of participants had the headache go away in 45 minutes?
75%
25%
62%
40%
What percent of the respondents were given the placebo and had their headache go away in 45 minutes?
75%
22%
40%
62%
A difference between an actual y-value and a predicted
y-value
Interpolation
Extrapolation
Correlations Coefficient
Residual
Is r = -0.87 strong, moderate, or weak?
strong
moderate
weak
Write the linear regression equation for the following data points. Round to the nearest tenth.
y=−0.27x+3.93
y=3.93x+−0.27
y=1.25x+3.75
y=0.27x+3.94
If x is temperature and y is coffee sales, use the following formula to determine the coffee sales on a 34° day.
y = -60x+6443
$4403
$4673
$8483
$6443
A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.
y = 1.5x + 12
y = 12x + 1.5
y = 0.67x - 8
y = -8x + 0.67
I. Random scatter in the residuals indicates a linear model.
II. If two variables are very strongly associated, then the correlation between them will be near 1 or -1.
III. Changing the units of measurement for x or y changes the correlation coefficient.
Interpret the slope of the Predicted line.
The linear model used to predict the distance traveled (in miles) given the time driven (in hours) is
We predict that for every mile driven, 61.93 hours has passed
We predict that for every mile driven, 1.79 hours has passed
We predict that for every hour driven, 1.79 miles is covered
We predict that for every hour driven, 61.93 miles is covered
What statistical test is appropriate for comparing the means of two independent groups?
Paired T-test
ANOVA
Independent T-test
Chi-square test
Which of the following is a correct interpretation of a 95% confidence interval for a population mean?
95% of the population mean falls within this interval.
We are 95% confident that the sample mean falls within this interval.
We are 95% confident that the population mean falls within this interval.
95% of the sample means will fall within this interval.
When conducting a hypothesis test, if the p-value is less than the significance level (alpha), what is the correct decision?
Fail to reject the null hypothesis.
Reject the null hypothesis.
Increase the sample size.
There is not enough information to make a decision.
