Textbook Problem

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The following results are for independent random samples taken from two populations.

Sample 1	Sample 2
n1 = 20	n2 = 30
${\bar{x}}_{\text{1}}=\text{2}2.5$	${\bar{x}}_{\text{2}}=\text{2}0.\text{1}$
s1 = 2.5	s2 = 4.8

1. a. What is the point estimate of the difference between the two population means?
2. b. What is the degrees of freedom for the t distribution?
3. c. At 95% confidence, what is the margin of error?
4. d. What is the 95% confidence interval for the difference between the two population means?

To determine

Find the point estimate of the difference between the two population means.

Explanation of Solution

Calculation:

The results of two independent random samples drawn from two populations are as follows:

Sample 1	Sample 2
$n_1=20$	$n_2=30$
${\overline{x}}_1=22.5$	${\overline{x}}_2=20.1$
$s_1=2.5$	$s_2=4$

To determine

Find the degrees of freedom for the t distribution.

To determine

Find the margin of error at 95% confidence.

To determine

Find the 95% confidence interval for the difference between the two population means.