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What is the most important reason that students buy from catalogs? The answer may differ for different groups of students. Here are results for separate random samples of American and Asian students at a large midwestern university:31(a) Should we use a chi-square test for homogeneity or a chi-square test of association/independence in this setting? Justify your answer.(b) State appropriate hypotheses for performing the type of test you chose in part (a). Minitab output from a chi-square test is shown below.(c) Check that the conditions for carrying out the test are met.(d) Interpret the P-value in context. What conclusion would you draw?

a. Chi-square test of homogeneityb. $H_{0} :$ There is no association between the variables$H_{a} :$ There is an association between the variablesc. See explanationd. There is sufficient evidence that there is an association.

Intro Stats / AP Statistics

Chapter 11

Inference for Distributions of Categorical Data

Section 2

Inference for Relationships

Confidence Intervals

The Chi-Square Distribution

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all right for this problem. So, you know, I had already written all this up. They made a slight mistake. So it's gonna read through what I had already written up. So in this one that we're considering people's preference, our justification behind buying, um, things through catalog and whether there were looking for this disco difference between it there a Asian or American securities Chi square test? Well, the data represents one sample. The subjects are classified by two things. Their answer and their ethnicity. So a chi square test for independence or association makes sense. The null hypothesis is that ethnicity and reasoning behind shopping via catalogs independent and make the alternate hypothesis just that they're not independent in regards to conditions, uh, samples a random sample. So that's good. In rights Independence, the sample size is less than 10% of the population being adults. So we treat the sample is being with replacement or, in other words, we can consider as independent observations. So, yeah, that's met. Randomness is met and then expected counts. If you look at the data given to you in the book, looks like the minimum expected Countess 5.13 which is less than or equal to five and greater than equal to five So expected counselor as well. So the conditions were met for a Chi Square test. They didn't give you a P value of 0.1 This is less than 0.5, that's We reject the null hypothesis, and we conclude the ethnicity and the justification behind shopping in a catalogue to not be independent.

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