Chapter 8.1, Problem 21P

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8th Edition

Charles Henry Brase + 1 other

ISBN: 9781337558075

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?

**(a)**

To determine

**To find:** A 95% confidence interval for

Explanation

**Calculation:**

Given that *x* distribution with sample mean *x* distribution has

We have to find 95% confidence interval,

**(b)**

To determine

**To find:** A 95% confidence interval for

**(c)**

To determine

**To find:** A 95% confidence interval for

**(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.

Sect-8.1 P-1PSect-8.1 P-2PSect-8.1 P-3PSect-8.1 P-4PSect-8.1 P-5PSect-8.1 P-6PSect-8.1 P-7PSect-8.1 P-8PSect-8.1 P-9PSect-8.1 P-10P

Sect-8.1 P-11PSect-8.1 P-12PSect-8.1 P-13PSect-8.1 P-14PSect-8.1 P-15PSect-8.1 P-16PSect-8.1 P-17PSect-8.1 P-18PSect-8.1 P-19PSect-8.1 P-20PSect-8.1 P-21PSect-8.1 P-22PSect-8.1 P-23PSect-8.1 P-24PSect-8.1 P-25PSect-8.2 P-1PSect-8.2 P-2PSect-8.2 P-3PSect-8.2 P-4PSect-8.2 P-5PSect-8.2 P-6PSect-8.2 P-7PSect-8.2 P-8PSect-8.2 P-9PSect-8.2 P-10PSect-8.2 P-11PSect-8.2 P-12PSect-8.2 P-13PSect-8.2 P-14PSect-8.2 P-15PSect-8.2 P-16PSect-8.2 P-17PSect-8.2 P-18PSect-8.2 P-19PSect-8.2 P-20PSect-8.2 P-21PSect-8.2 P-22PSect-8.2 P-23PSect-8.3 P-1PSect-8.3 P-2PSect-8.3 P-3PSect-8.3 P-4PSect-8.3 P-5PSect-8.3 P-6PSect-8.3 P-7PSect-8.3 P-8PSect-8.3 P-9PSect-8.3 P-10PSect-8.3 P-11PSect-8.3 P-12PSect-8.3 P-13PSect-8.3 P-14PSect-8.3 P-15PSect-8.3 P-16PSect-8.3 P-17PSect-8.3 P-18PSect-8.3 P-19PSect-8.3 P-20PSect-8.3 P-21PSect-8.3 P-22PSect-8.3 P-23PSect-8.3 P-24PSect-8.3 P-25PSect-8.3 P-26PSect-8.3 P-27PSect-8.3 P-28PCh-8 P-1CRCh-8 P-2CRCh-8 P-3CRCh-8 P-4CRCh-8 P-5CRCh-8 P-6CRCh-8 P-7CRCh-8 P-8CRCh-8 P-9CRCh-8 P-10CRCh-8 P-11CRCh-8 P-12CRCh-8 P-13CRCh-8 P-14CRCh-8 P-15CRCh-8 P-16CRCh-8 P-17CRCh-8 P-1DHGPCh-8 P-2DHGPCh-8 P-3DHGPCh-8 P-1LCWPCh-8 P-2LCWPCh-8 P-3LCWP

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