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Chapter 8: Q.3.2 (page 494)

1. In the company’s prior-year survey, 80% of customers surveyed said they were “satisfied” or “very satisfied.” Using this value as a guess for pˆ, 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

≈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

What critical value t⋆from Table B would you use for a 90%confidence interval for the population mean based on an SRS of size 77? If possible, use technology to find a more accurate value of t⋆. What advantage does the more accurate df provide?

Do you go to church? The Gallup Poll plans to ask a random sample of adults whether they attended a religious service in the last 7days. How large a sample would be required to obtain a margin of error of 0.01ina99%confidence interval for the population proportion who would say that they attended a religious service? Show your work.

- Construct and interpret a confidence interval for a population proportion.

- Explain how practical issues like nonresponse, under coverage, and response bias can affect the interpretation of a confidence interval.

It's about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.

(a) Increasing the confidence level

(b) Quadrupling the sample size

You have an SRS of 23 observations from a Normally distributed population. What critical value would you use to obtain a 98% confidence interval for the mean M of the population if S is unknown?

(a) 2.508

(b) 2.500

(c) 2.326

(d) 2.183

(e) 2.177

I collect an SRS of size n from a population and compute a 95%confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?

(a) Use a larger confidence level.

(b) Use a smaller confidence level.

(c) Increase the sample size.

(d) Use the same confidence level, but compute the interval n times. Approximately5% of these intervals will be larger.

(e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is 0.05.
See all solutions

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