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Chapter 11: Q. 2.3 (page 684)
Let鈥檚 continue our analysis of Joey鈥檚 sample of M&M鈥橲 Peanut Chocolate Candies from the previous Check Your Understanding (page 681).
3. Use Table C to find the P-value. Then use your calculator鈥檚 cdf command.
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32. How are schools doing? Refer to Exercises 28 and 30 .
(a) Check that the conditions for performing the chi-square test are met.
(b) Use Table to find the -value. Then use your calculator's command.
(c) Interpret the -value from the calculator in context.
(d) What conclusion would you draw? Justify your answer.
An appropriate null hypothesis to test whether the trees in the forest are randomly distributed is
(a) , where the mean number of trees in each quadrant.
(b) , where the proportion of all trees in the forest that are in Quadrant
(c) , where is the number of trees from the sample in Quadrant .
(d) , where is the actual proportion of trees in the forest that are in Quadrant .
(e) , where is the proportion of trees in the sample that are in Quadrant
Gastric freezing was once a recommended treatment for ulcers in the upper intestine. The use of gastric freezing stopped after experiments showed it had no effect. One randomized comparative experiment found that of the gastric-freezing patients improved, while of the patients in the placebo group improved. We can test the hypothesis of 鈥渘o difference鈥� in the effectiveness of the treatments 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: Gastric freezing, Placebo 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).
The conditions for carrying out the chi-square test in exercise T11.2 are
I. Separate random samples from the populations of interest.
II. Expected counts large enough.
III. The samples themselves and the individual observations in each sample are independent.
Which of the conditions is (are) satisfied in this case?
(a) I only
(d) Il and III only
(b) II only
(e) I, II, and III
(c) I and II only
Skittles Statistics teacher Jason Molesky contacted Mars, Inc., to ask about the color distribution for Skittles candies. Here is an excerpt from the response he received: 鈥淭he original flavor blend for the SKITTLES BITE SIZE CANDIES is lemon, lime, orange, strawberry, and grape. They were chosen as a result of consumer preference tests we conducted. The flavor blend is 20 percent of each flavor.鈥�
(a) State appropriate hypotheses for a significance test of the company鈥檚 claim.
(b) Find the expected counts for a bag of Skittles with 60 candies.
(c) How large a C2 statistic would you need to get in order to have significant evidence against the company鈥檚 claim at the A 0.05 level? At the A 0.01 level?
(d) Create a set of observed counts for a bag with 60 candies that gives a P-value between 0.01 and 0.05. Show the calculation of your chi-square statistic.
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