   Chapter 8.1, Problem 21P ### Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
ISBN: 9781337558075

#### Solutions

Chapter
Section ### Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
ISBN: 9781337558075
Textbook Problem

# Confidence 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?

(a)

To determine

To find: A 95% confidence interval for μ based on the sample of size 49. Also, find the margin of error.

Explanation

Calculation:

Given that x distribution with sample mean x¯=30 and sample size n=49. Supposing that the x distribution has σ=12

We have to find 95% confidence interval,

c=0.95UsingTable3ofAppendixz0.95=1.96σ=12n=49E=zcσnE=1

(b)

To determine

To find: A 95% confidence interval for μ based on the sample of size 100. Also, find the margin of error.

(c)

To determine

To find: A 95% confidence interval for μ based on the sample of size 225. Also, find the margin of error.

(d)

To determine

The comparison of the margins of error for parts (a) through (c) and determines whether the margin of error decrease as the value of the sample size increases.

(e)

To determine

The comparison of confidence interval for part (a) through (c). Also determine whether the length of confidence interval decreases as the value of the sample size increases.

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