Review
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Decide whether or not the conditions and assumptions for inference with the two -proportion z-test are satisfied.
Explain your answer.
1) An Illinois study examined the effect of day care on behavior in toddlers. Randomly selected parents who had
a toddler in full-time day care were asked if their child had behavioral problems. The researchers found that
among 987 parents surveyed, 212 said their child had behavioral problems. Among 349 randomly selected
parents with a toddler at home, 17 reported that their child had behavioral problems.
Construct the indicated confidence interval for the difference in proportions. Assume that the samples are independent
and that they have been randomly selected.
2) A survey of randomly chosen adults found that 36 of the 63 women and 42 of the 73 men follow regular
exercise programs. Construct a 95% confidence interval for the difference in the proportions of women and
men who have regular exercise programs.
3) In a random sample of 500 people aged 20 -24, 22% were smokers. In a random sample of 450 people aged
25-29, 14% were smokers. Construct a 95% confidence interval for the difference in smoking rates for the two
groups.
Interpret the given confidence interval.
4) Suppose the proportion of women who follow a regular exercise program is pw and the proportion of men
who follow a regular exercise program is pm . A study found a 90% confidence interval for pw - pm is (
-0.025, 0.113). Give an interpretation of this confidence interval.
Construct the indicated confidence interval for the difference between the two population means. Assume that the
assumptions and conditions for inference have been met.
5) Two types of flares are tested for their burning times (in minutes) and sample results are given below.
Brand X
Brand Y
n = 35
n = 40
x = 19.4
s = 1.4
x = 15.1
s = 0.8
Construct a 95% confidence interval for the difference μX - μY based on the sample data.
Use the paired t-interval procedure to obtain the required confidence interval for the mean difference. Assume that the
conditions and assumptions for inference are satisfied.
6) An agricultural company wanted to know if a new insecticide would increase corn yields. Eight test plots
showed an average increase of 3.125 bushels per acre. The standard deviation of the increases was 2.911
bushels per acre. Determine a 99% confidence interval for the mean increase in yield.
7) Ten different families are tested for the number of gallons of water a day they use before and after viewing a
conservation video. Construct a 90% confidence interval for the mean of the difference of the ʺbeforeʺ minus the
ʺafterʺ times if d(after-before) = -4.8 and sd=5.2451
Before 33 33 38 33 35 35 40 40 40 31
After 34 28 25 28 35 33 31 28 35 33
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Construct the indicated confidence interval for the difference between the two population means. Assume that the
assumptions and conditions for inference have been met.
8) A researcher was interested in comparing the salaries of female and male employees of a particular company.
Independent random samples of 8 female employees (sample 1) and 15 male employees (sample 2) yielded the
following weekly salaries (in dollars).
Female
495
760
556
904
520
1005
743
660
Male
722
562
880
520
500
1250
750
1640
518
904
1150
805
480
970
605
Determine a 98% confidence interval for the difference, μ - μ , between the mean weekly salary of all
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female employees and the mean weekly salary of all male employees.
Interpret the given confidence interval.
9) Ten different families were tested for the average number of gallons of water they used per day before and
after viewing a conservation video. A 90% confidence interval for the difference of the means after and before
the training, μA - μB, was determined to be (-10.3, -4.1).
Construct the indicated confidence interval for the difference in proportions. Assume that the samples are independent
and that they have been randomly selected.
10) A survey of randomly selected college students found that 50 of the 95 freshmen and 52 of the 107 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.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
11) A survey asked people ʺOn what percent of days do you get more than 30 minutes of vigorous exercise?ʺ Using
their responses we want to estimate the difference in exercise frequency between men and women. We should
use a
A) matched pairs t-interval
B) 2-proportion z-interval
C) 2-sample t-interval
D) 1-sample t-interval
E) 1-proportion z-interval
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Answer Key
Testname: UNTITLED1
1) The assumptions and conditions necessary for inference are satisfied. The samples are both random. Each sample
contains less than 10% of the population. The samples are independent of each other. There are at least 10 successes
and at least 10 failures in each sample.
2) (-0.171, 0.163)
3) (0.032, 0.128)
4) We are 90% confident that the proportion of women who follow a regular exercise program is between 2.5% less and
11.3% more than the proportion of men who follow a regular exercise program.
5) (3.8, 4.8)
6) (-0.476, 6.726)
7) (1.8,7.8)
8) (-$382, $158)
9) Based on this sample, we are 90% confident that the average decrease in daily water consumption after viewing the
conservation video is between 4.1 and 10.3 gallons.
10) (-0.124, 0.204)
11) C
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