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Chapter 11: Q. 49 (page 756)

Where do young adults live? A survey by the National Institutes of Health asked a random sample of young adults (aged 19to 25years), 鈥淲here do you live now? That is, where do you stay most often?鈥� Here is the full two-way table (omitting a few who refused to answer and one who reported being homeless):

a. Should we use a chi-square test for homogeneity or a chi-square test for independence in this setting? Justify your answer.

b. State appropriate hypotheses for performing the type of test you chose in part (a). Here is Minitab output from a chi-square test.

c. Check that the conditions for carrying out the test are met.

d. Interpret the P-value. What conclusion would you draw?

Short Answer

Expert verified

a. We should use Chi-square test for independence.

b. H0: Gender has nothing to do with where you reside.

Ha:Gender and place of residence are linked.

c. The chi square test has three conditions: randomness, independence, and large counts. Because the sample was chosen at random, the random sample condition was met.

d. There is convincing evidence that the association between gender and living location

Step by step solution

01

Part (a) Step 1 : Given Information

We have to determine which chi-square test is appropriate for given setting.

02

Part (a) Step 2 : Simplification

First, we must determine which test should be used in a certain case. There are three tests to complete:
Chi-square goodness-of-fit test, chi-square homogeneity test, and chi-square independence test All of these tests will be detailed for us. A chi-square goodness-of-fit test is used when we are interested in the distribution of a single variable. In this circumstance, we must employ a chi-square test for homogeneity when we are interested in the distribution of two variables with numerous independent samples. We would like to do a chi-square test for independence when we are interested in the distribution of two variables and there is only one sample. We are given two variables for a certain setting: Gender and place of residence There is only one random sample available.
Asaresult,weshouldperformtheChi-squaretesttodetermineindependence.
03

Part (b) Step 1 : Given Information

We have to state the null and alternative hypotheses.

04

Part (b) Step 2 : Simplification

The following are the null and alternate hypotheses:
H0: Gender has nothing to do with where you reside.
Ha: Gender and where you reside have a connection.
05

Part (c) Step 1 : Given Information

We have to verify the conditions for inference.

06

Part (c) Step 2 : Simplification

Thechisquaretesthasthreeconditions:randomness,independence,andlargecounts.
Because the sample was chosen at random, the random sample condition was met.
Because the sample size is less than 10%of the total population, the requirement of independence is met.
Because each survey's projected count is at least 5, the criterion of a large count is met.
07

Part (d) Step 1 : Given Information

We have to explain conclusion.

08

Part (d) Step 2 : Simplification

The p-value = 0.012. If there is no relationship between the two variables, the probability of getting a sample that is similar to or more extreme than the given sample is 0.012or 1.2percent.H0is rejected because the P-value is less than 0.05.
Conclusion: There is strong evidence that there is a link between gender and where you live.

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Most popular questions from this chapter

Which test? Determine which chi-square test is appropriate in each of the following settings. Explain your reasoning.

a. With many babies being delivered by planned cesarean section, Mrs. McDonald鈥檚 statistics class hypothesized that there would be fewer younger people born on the weekend. To investigate, they selected a random sample of people born before1980 and a separate random sample of people born after1993. In addition to year of birth, they also recorded the day of the week on which each person was born.

b. Are younger people more likely to be vegan/vegetarian? To investigate, the Pew Research Center asked a random sample of 1480 U.S. adults for their age and whether or not they are vegan/vegetarian.

Birds in the trees Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, 54% of the trees are Douglas firs, 40% are ponderosa pines, and 6% are other types of trees. At a randomly selected time during the day, the researchers observed 156 red-breasted nuthatches: 70 were seen in Douglas firs, 79 in ponderosa pines, and 7 in other types of trees.

a. Do these data provide convincing evidence that nuthatches prefer particular types of trees when they鈥檙e searching for seeds and insects?

b. Relative to the proportion of each tree type in the forest, which type of trees do the nuthatches seem to prefer the most? The least?

Where do you live? Conduct a follow-up analysis for the test in Exercise 49.

Is astrology scientific? The General Social Survey (GSS) asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two-way table of counts for people in the sample who had three levels of higher education:

a. State appropriate hypotheses for performing a chi-square test for independence in this setting.

b. Compute the expected counts assuming that H0is true.

c. Calculate the chi-square test statistic, df, and P-value.

d. What conclusion would you draw?

Popular kids Who were the popular kids at your elementary school? Did they get good grades or have good looks? Were they good at sports? A study was performed in Michigan to examine the factors that determine social status for children in grades 4,5,and 6. Researchers administered a questionnaire to a random sample of 478students in these grades. One of the questions asked, "What would you most like to do at school: make good grades, be good at sports, or be popular?" The two-way table summarizes the students' responses. Is there convincing evidence of an association between gender and goal for students in grades 4,5,and 6?
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