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# In a random sample of 150 customers of a high-speed ISBN: 9780073401331 38

## Solution for problem 12E Chapter 5.2

Statistics for Engineers and Scientists | 4th Edition

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Problem 12E

In a random sample of 150 customers of a high-speed internet provider, 63 said that their service had been interrupted one or more times in the past month.

a. Find a 95% confidence interval for the proportion of customers whose service was interrupted one or more times in the past month.

b. Find a 99% confidence interval for the proportion of customers whose service was interrupted one or more times in the past month.

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 99% confidence interval to specify the proportion to within ±0.05.

Step-by-Step Solution:

Step 1 of 5:

Suppose that, a random sample of 150 customers of a high-speed internet provider, 63 said that their service had been interrupted one or more times in the past month.

Here,

x = 63, n = 150

Step 2 of 5:

a). Here we have to find a 95% confidence interval for the proportion of customers whose service was interrupted one or more times in the past month.

Then, = 150+ 4

= 154. = = 0.4221

A 95% confidence interval for ‘p’ is given by  For a 95% confidence interval: Z - value for 95% confidence interval is Then,   (0.3441, 0.5001)

Therefore, a 95% confidence interval for the proportion of customers whose service was interrupted one or more times in the past month is (0.3441, 0.5001).

Step 3 of 5:

b). We need to find a 99% confidence interval for the proportion of customers whose service was interrupted one or more times in the past month.

Then, = 150+ 4

= 154. = = 0.4221

A 99% confidence interval for ‘p’ is given by  For a 99% confidence interval: Z - value for 99% confidence interval is Then,  = 0.4221 0.1027

(0.3194, 0.5248)

Therefore, a 99% confidence interval for the proportion of customers whose service was interrupted one or more times in the past month is (0.3194, 0.5248).

Step 4 of 5

Step 5 of 5

##### ISBN: 9780073401331

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