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Chapter 8: Q.3.2 (page 494)

1. In the company鈥檚 prior-year survey, 80% of customers surveyed said they were 鈥渟atisfied鈥� or 鈥渧ery satisfied.鈥� Using this value as a guess for p藛, find the sample size needed for a margin of error of 3% at a 95% confidence level.

What if the company president demands 99% confidence instead? Determine how this would affect your answer to Question 1.

Short Answer

Expert verified

The required sample size is 1180.

From the calculations, we know that the increase in confidence level is leading to an increase in the sample size.

Step by step solution

01

Given Information

Given that

Population proportion(p^)=80%=0.80

Margin of error(E)=3%=0.03

Confidence level=95%

02

Explanation

From the standard normal table, thez-score at 99%the confidence level is 2.579

The sample size is calculated as:

n=(p^)(1-p^)zE2

=0.80(1-0.80)2.5760.032

=1179.537

鈮�1180

Thus, the required sample size is 1180.

From the calculations, we know that the increase in confidence level is leading to an increase in the sample size.

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Most popular questions from this chapter

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