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Chapter 11: Q. 2.3 (page 684)
Let’s continue our analysis of Joey’s sample of M&M’S Peanut Chocolate Candies from the previous Check Your Understanding (page 681).
3. Use Table C to find the P-value. Then use your calculator’s cdf command.
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The General Social Survey asked a random sample of adults, “Do you favour or oppose the death penalty for persons convicted of murder?” The following table gives the responses of people whose highest education was a high school degree and of people with a bachelor’s degree:
We can test the hypothesis of “no difference” in support for the death penalty among people in these educational categories in two ways: with a two-sample z test or with a chi-square test.
(a) Minitab output for a chi-square test is shown below. State appropriate hypotheses and interpret the P-value in context. What conclusion would you draw? Chi-Square Test: C1, C2 Expected counts are printed below-observed counts Chi-Square contributions are printed below expected counts
(b) Minitab output for a two-sample z test is shown below. Explain how these results are consistent with the test in part (a).
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
(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?
Which hypotheses would be appropriate for performing a chi-square test?
(a) The null hypothesis is that the closer students get to graduation, the less likely they are to be opposed to tuition increases. The alternative is that how close students are to graduation makes no difference in their opinion.
(b) The null hypothesis is that the mean number of students who are strongly opposed is the same for each of the four years. The alternative is that the mean is different for at least two of the four years.
(c) The null hypothesis is that the distribution of student opinion about the proposed tuition increase is the same for each of the four years at this university. The alternative is that the distribution is different for at least two of the four years.
(d) The null hypothesis is that year in school and student opinion about the tuition increase in the sample are independent. The alternative is that these variables are dependent.
(e) The null hypothesis is that there is an association between a year in school and opinion about the tuition increase at this university. The alternative hypothesis is that these variables are not associated.
Mars, Inc., reports that their M&M’S Peanut Chocolate Candies are produced according to the following color distribution: each of blue and orange, each of green and yellow, and each of red and brown. Joey bought a bag of Peanut Chocolate Candies and counted the colors of the candies in his sample: blue, orange,green, yellow, red, and brown.
State appropriate hypotheses for testing the company’s claim about the color distribution of peanut .
Calculate the chi-square statistic for Joey’s sample. Show your work
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