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A soft-drink manufacturer purchases aluminum cans from an

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 3E Chapter 5.2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 3E

A soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 70 cans is selected from a large shipment, and each is tested for strength by applying an increasing load to the side of the can until it punctures. Of the 70 cans, 52 meet the specification for puncture resistance.

a. Find a 95% confidence interval for the proportion of cans in the shipment that meet the specification.

b. Find a 90% confidence interval for the proportion of cans in the shipment that meet the specification.

c. Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.05.

d. Find the sample size needed for a 90% confidence interval to specify the proportion to within ±0.05.

e. If a 90% confidence interval is computed each day for 300 days, what is the probability that more than 280 of the confidence intervals cover the true proportions?

Step-by-Step Solution:

Solution:

Step 1 of 4:

A random sample of 70 cans is selected from a large shipment, and each is tested for strength by applying an increasing load to the side of the can until it punctures. It is observed that among 70 cans 52 meet the specification for puncture resistance.

We have to find

  1. 95 % CI for the proportion of cans in the shipment that meet the specification.
  2.  90 % CI for the proportion of cans in the shipment that meet the specification
  3.  The sample size needed for 95% CI to specify the proportion with in  .
  4.  The sample size needed for 90% CI to specify the proportion with in  .
  5.  Probability that more than 280 of the confidence intervals cover the true proportion.

Step 2 of 3

Chapter 5.2, Problem 3E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “A soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 70 cans is selected from a large shipment, and each is tested for strength by applying an increasing load to the side of the can until it punctures. Of the 70 cans, 52 meet the specification for puncture resistance.a. Find a 95% confidence interval for the proportion of cans in the shipment that meet the specification.________________b. Find a 90% confidence interval for the proportion of cans in the shipment that meet the specification.________________c. Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.05.________________d. Find the sample size needed for a 90% confidence interval to specify the proportion to within ±0.05.________________e. If a 90% confidence interval is computed each day for 300 days, what is the probability that more than 280 of the confidence intervals cover the true proportions?” is broken down into a number of easy to follow steps, and 149 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 3E from chapter: 5.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 3E from 5.2 chapter was answered, more than 1131 students have viewed the full step-by-step answer. This full solution covers the following key subjects: confidence, cans, interval, Find, proportion. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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A soft-drink manufacturer purchases aluminum cans from an