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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
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A candy manufacturer selects mints at random from the production line and weighs them

Chapter 7, Problem 7.3-10

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QUESTION:

A candy manufacturer selects mints at random from the production line and weighs them. For one week, the day shift weighed n1 = 194 mints and the night shift weighed n2 = 162 mints. The numbers of these mints that weighed at most 21 grams was y1 = 28 for the day shift and y2 = 11 for the night shift. Let p1 and p2 denote the proportions of mints that weigh at most 21 grams for the day and night shifts, respectively. (a) Give a point estimate of p1. (b) Give the endpoints for a 95% confidence interval for p1. (c) Give a point estimate of p1 p2. (d) Find a one-sided 95% confidence interval that gives a lower bound for p1 p2.

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QUESTION:

A candy manufacturer selects mints at random from the production line and weighs them. For one week, the day shift weighed n1 = 194 mints and the night shift weighed n2 = 162 mints. The numbers of these mints that weighed at most 21 grams was y1 = 28 for the day shift and y2 = 11 for the night shift. Let p1 and p2 denote the proportions of mints that weigh at most 21 grams for the day and night shifts, respectively. (a) Give a point estimate of p1. (b) Give the endpoints for a 95% confidence interval for p1. (c) Give a point estimate of p1 p2. (d) Find a one-sided 95% confidence interval that gives a lower bound for p1 p2.

ANSWER:

Step 1 of 5

Given:

The sample number of mints of the day shift is   = 194 mints.

The sample number of mints of the night shift is  = 162 mints.

For the day shift, the numbers of mints that weighed at most 21 grams is  = 28 .

For the night shift, the numbers of mints that weighed at most 21 grams is  = 11 .

 and  represents the proportions of mints that weigh at most 21 grams for the day and night shifts, respectively.

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