Math

StatisticsUnderstanding Basic StatisticsConfidence Intervals: Sample Size A random sample is drawn from a population with σ = 12. The sample mean is 30. (a) Compute a 95% confidence interval for µ based on a sample of size 49. What is the value of the margin of error? (b) Compute a 95% confidence interval for µ based on a sample of size 100. What is the value of the margin of error? (c) Compute a 95% confidence interval for µ based on a sample of size 225. What is the value of the margin of error? (d) Compare the margins of error for parts (a) through (c). As the sample size increases, does the margin of error decrease? (e) Critical Thinking Compare the lengths of the confidence intervals for parts (a) through (c). As the sample size increases, does the length of a 90% confidence interval decrease?BuyFind*arrow_forward*

8th Edition

Charles Henry Brase + 1 other

Publisher: Cengage Learning

ISBN: 9781337558075

Chapter 8.1, Problem 21P

Textbook Problem

**Confidence Intervals: Sample Size** A random sample is drawn from a population with
*=* 12. The sample mean is 30.

(a) Compute a 95% confidence interval for µ based on a sample of size 49. What is the value of the margin of error?

(b) Compute a 95% confidence interval for µ based on a sample of size 100. What is the value of the margin of error?

(c) Compute a 95% confidence interval for µ based on a sample of size 225. What is the value of the margin of error?

(d) Compare the margins of error for parts (a) through (c). As the sample size increases, does the margin of error decrease?

(e)**Critical Thinking** Compare the lengths of the confidence intervals for parts (a) through (c). As the sample size increases, does the length of a 90% confidence interval decrease?

Understanding Basic Statistics

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