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# Let p equal the proportion of yellow candies in a package

ISBN: 9780321923271 41

## Solution for problem 12E Chapter 8.3

Probability and Statistical Inference | 9th Edition

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Problem 12E

PROBLEM 12E

Let p equal the proportion of yellow candies in a package of mixed colors. It is claimed that p = 0.20.

(a) Define a test statistic and critical region with a significance level of α = 0.05 for testing H0: p = 0.20 against a two-sided alternative hypothesis.

(b) To perform the test, each of 20 students counted the number of yellow candies, y, and the total number of candies, n, in a 48.1-gram package, yielding the following ratios, y/n: 8/56, 13/55, 12/58, 13/56, 14/57, 5/54,14/56, 15/57, 11/54, 13/55, 10/57, 8/59, 10/54, 11/55, 12/56, 11/57, 6/54, 7/58, 12/58, 14/58. If each individual tests H0: p = 0.20, what proportion of the students rejected the null hypothesis?

(c) If we may assume that the null hypothesis is true, what proportion of the students would you have expected to reject the null hypothesis?

(d) For each of the 20 ratios in part (b), a 95% confidence interval for p can be calculated. What proportion of these 95% confidence intervals contain p = 0.20?

(e) If the 20 results are pooled so that equals the total sample size, do we reject H0: p = 0.20?.

Step-by-Step Solution:

Chapter 8 - Hypothesis Testing ● Step 1: Restate the research question as a hypothesis with a null hypothesis about the populations ● make a claim about the population ○ the null hypothesis ○ H0 ● determine a relevant alternative claim ○ the alternative hypothesis ○ H1 ● Step 2: determine characteristics of the comparison distribution ○ represents the population situation if the null hypothesis is true ○ it is the distribution you are comparing your sample to ●

Step 3 of 3

##### ISBN: 9780321923271

Since the solution to 12E from 8.3 chapter was answered, more than 324 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 12E from chapter: 8.3 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This full solution covers the following key subjects: hypothesis, proportion, candies, students, null. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. The answer to “Let p equal the proportion of yellow candies in a package of mixed colors. It is claimed that p = 0.20.(a) Define a test statistic and critical region with a significance level of ? = 0.05 for testing H0: p = 0.20 against a two-sided alternative hypothesis.(b) To perform the test, each of 20 students counted the number of yellow candies, y, and the total number of candies, n, in a 48.1-gram package, yielding the following ratios, y/n: 8/56, 13/55, 12/58, 13/56, 14/57, 5/54,14/56, 15/57, 11/54, 13/55, 10/57, 8/59, 10/54, 11/55, 12/56, 11/57, 6/54, 7/58, 12/58, 14/58. If each individual tests H0: p = 0.20, what proportion of the students rejected the null hypothesis?(c) If we may assume that the null hypothesis is true, what proportion of the students would you have expected to reject the null hypothesis?(d) For each of the 20 ratios in part (b), a 95% confidence interval for p can be calculated. What proportion of these 95% confidence intervals contain p = 0.20?(e) If the 20 results are pooled so that equals the total sample size, do we reject H0: p = 0.20?.” is broken down into a number of easy to follow steps, and 187 words. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9.

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