Statistics
Review questions for Test-4
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Construct the indicated confidence interval for the difference in proportions. Assume that the samples are independent
and that they have been randomly selected.
1)
A survey of randomly selected college students found that
56
of the
103
freshmen and
88
of the
124
sophomores
surveyed had purchased used textbooks in the past year. Construct a 98% confidence interval for the difference
in the proportions of college freshmen and sophomores who purchased used textbooks.
Interpret the given confidence interval.
2)
Suppose the proportion of sophomores at a particular college who purchased used textbooks in the past year is
ps and the proportion of freshmen at the college who purchased used textbooks in the past year is pf. A study
found a 98% confidence interval for ps - pf is (0.233, 0.423). Give an interpretation of this confidence interval.
Use a two proportion z-test to perform the required hypothesis test. State the conclusion.
3)
Use the given sample data to test the claim that p
1
< p
2
. Use a significance level of 0.10.
Sample 1 Sample 2
n1 = 462 n2 = 380
x1 = 84 x2 = 95
Using the t-tables, software, or a calculator, estimate the critical value of t for the given confidence interval and degrees
of freedom.
4)
90% confidence interval with df = 4.
Use the given sample data to construct the indicated confidence interval for the population mean.
5)
A random sample of 30 households was selected from a particular neighborhood. The number of cars for each
household is shown below. Estimate the mean number of cars per household for the population of households
in this neighborhood. Give the 95% confidence interval.
2 0 1 2 3 2 1 0 1 4
1 3 2 0 1 1 2 3 1 2
1 0 0 4 1 2 2 1 0 2
Interpret the confidence interval.
6)
A credit union took a random sample of 40 accounts and yielded the following 90% confidence interval for the
mean checking account balance at the institution: $2196 < m(balance) < $3830.
Test the given claim by using the P-value method of testing hypotheses. Assume that the sample is a simple random
sample selected from a normally distributed population. Include the hypotheses, the test statistic, the p-value, and your
conclusion.
7)
Test the claim that the mean lifetime of car engines of a particular type is greater than 220,000 miles.
Sample
data are summarized as n = 23, x = 226,450 miles, and s = 11,500 miles. Use a significance level of a = 0.01.
Find the necessary sample size.
8)
Scores on a certain test are normally distributed with a variance of
47
. A researcher wishes to estimate the mean
score achieved by all adults on the test. Find the sample size needed to assure with 98 percent confidence that
the sample mean will not differ from the population mean by more than 5 units.
1
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