a. Explanation With reference to Exercise 14.8, p 1 = 9 16 , p 2 = 3 16 , p 3 = 3 16 , p 4 = 1 16 . With reference to Exercise 14.6, Part (6), the large sample ( 1 − α ) 100 % confidence interval is given as follows: ( 1 − α ) 100 % confidence interval = p ^ i − p ^ j ± z α 2 p ^ i ( 1 − p ^ i ) + p ^ j ( 1 − p ^ j ) + 2 p ^ i p ^ j n Critical value: In context, the level of the test α is 0.05. Here, the alternative is two-tailed test. Hence, the rejection region will be z < − z 0.05 2 or z > z 0.05 2 . From “Appendix 3, Table 4 Normal curve areas”, the critical value under the level of significance 0.025 is 1.96. Thus, the rejection region under the level of significance of 0.05 is z < − 1.96 or z > 1.96 . Substitute the corresponding values to get the 95% confidence interval b. To determine Construct the simultaneous confidence interval to compare the proportion of round yellow peas with the proportions other three categories.

Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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Chapter 14.3, Problem 9E

To determine

Obtain and interpret the 95% confidence interval for the difference in the proportions of round yellow and round green peas.

To determine

Construct the simultaneous confidence interval to compare the proportion of round yellow peas with the proportions other three categories.

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Chapter 14 Solutions

Mathematical Statistics with Applications

Ch. 14.3 - Historically, the proportions of all Caucasians in...Ch. 14.3 - Prob. 2E Ch. 14.3 - Prob. 3E Ch. 14.3 - Prob. 4E Ch. 14.3 - Prob. 5E Ch. 14.3 - Prob. 6E Ch. 14.3 - Prob. 7E Ch. 14.3 - Prob. 8E Ch. 14.3 - Prob. 9E Ch. 14.3 - Prob. 10E

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Obtain and interpret the 95% confidence interval for the difference in the proportions of round yellow and round green peas.

Solution Summary: The author explains that the 95% confidence interval for the difference in the proportions of round yellow and round green peas is (0.241,0.539).

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Obtain and interpret the 95% confidence interval for the difference in the proportions of round yellow and round green peas.

Construct the simultaneous confidence interval to compare the proportion of round yellow peas with the proportions other three categories.

Chapter 14 Solutions