AP Statistics 10.1A Activity
Comparing Samples
Name ______________________
Per _____ Date _______________
Are Toyota or Nissan owners more satisfied with their vehicles? Let’s design a study to find out. We’ll select a
random sample of 400 Toyota owners and a separate random sample of 400 Nissan owners. Then we’ll ask
each individual in the sample: “Would you say that you are generally satisfied with your (Toyota/Nissan)
vehicle?”
_____ 1.) Is this a problem about comparing means or comparing proportions?
(a) means
(b) proportions
_____ 2.) What type of study design is being used to produce data?
(a) observational study
(b) census
(c) completely randomized experiment
(d) cluster
(e) stratified random
(f) block
A bank wants to know which of two incentive plans will most increase the use of its credit cards. It offers each
incentive to a group of current credit card customers, determined at random, and compares the amount
charged during the following six months.
_____ 3.) Is this a problem about comparing means or comparing proportions?
(a) means
(b) proportions
_____ 4.) What type of study design is being used to produce data?
(a) observational study
(b) census
(c) completely randomized experiment
(d) cluster
(e) stratified random
(f) block
A candy maker offers Child and Adult bags of jelly beans with different color mixes. The company claims that
the Child mix has 30% red jelly beans while the Adult mix contains 15% red jelly beans. Assume that the candy
maker’s claim is true. Suppose we take a random sample of 50 jelly beans from the Child mix and a separate
random sample of 100 jelly beans from the Adult mix.
5.) What is the shape of the sampling distribution child - adult?
6.) What is the mean of the sampling distribution child - adult?
7.) What is the standard deviation of the sampling distribution child - adult?
8.) Find the probability that the proportion of red jelly beans in the Child sample is less than or equal to the
proportion of red jelly beans in the Adult sample.
9.) Suppose that the Child and Adult samples contain an equal proportion of red jelly beans. Based on your
result in previous problem, would this give you reason to doubt the company’s claim?
A researcher reports that 80% of high school graduates but only 40% of high school dropouts would pass a
basic literacy test. Assume that the researcher’s claim is true. Suppose we give a basic literacy test to a
random sample of 60 high school graduates and a separate random sample of 75 high school dropouts.
10.) What is the shape of the sampling distribution graduate - dropout?
11.) What is the mean of the sampling distribution graduate - dropout?
12.) What is the standard deviation of the sampling distribution graduate - dropout?
13.) Find the probability that the proportion of graduates who pass the test is at least 0.20 higher than the
proportion of dropouts who pass.
14.) Suppose that the difference in the sample proportions (graduate – dropout) who pass the test is exactly
0.20. Based on your result in number 13, would this give you reason to doubt the researcher’s claim?
_____ 15.) According to Humane Society data, 39% of households in the United States have at least one dog.
In the United Kingdom, 23% of households have at least one dog. Suppose you select an SRS of 75
households in the U.S. and 80 households in the U.K. Which of the following best describes the sampling
distribution of proportions for United States - United Kingdom?
(a)
(b)
(c)
(d)
(e)
Mean = 0.16, Standard deviation = 0.024, Shape unknown
Mean unknown, Standard deviation unknown, Shape approximately Normal.
Mean = 0.16, Standard deviation = 0.024, Shape unknown
Mean unknown, Standard deviation unknown, Shape approximately Normal.
Mean = 0.16, Standard deviation = 0.073, Shape approximately Normal.
_____ 16.) According to recent polls, 24% of people in the United States answered Yes to the question, “Did
you smoke any form of tobacco yesterday?” In the European Union, 28% of people answered yes to a similar
question. Let’s assume these are population parameters for the two populations. If you select a simple random
sample of 40 people in the U.S. and 50 people in the E.U., which of the following expressions represents the
standard deviation of the sampling distribution for the difference in the proportion of smokers in the two
groups?