Question

In order to use a 90% confidence interval to compare admission exam scores for sophomores (group #1) and freshmen (group #2), two independent random samples were selected. The results showed:

1-Sophomores: Sample mean = 85, sample standard deviation = 10, sample size = 50.

2-Freshmen: Sample mean = 78, sample standard deviation = 12, sample size = 72.

For forming a 90% confidence interval for μ 1 − μ 2, the standard error is __________ .

Group of answer choices

12

2

None of the other choices represent a suitable response.

10

4

Answer 1

using excel>addin>phstat<two sample test

we have

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.1
Population 1 Sample
Sample Size	50
Sample Mean	85
Sample Standard Deviation	10
Population 2 Sample
Sample Size	72
Sample Mean	18
Sample Standard Deviation	12
standard error	2.066671
Intermediate Calculations
Population 1 Sample Degrees of Freedom	49
Population 2 Sample Degrees of Freedom	71
Total Degrees of Freedom	120
Pooled Variance	126.0333
Difference in Sample Means	67
t Test Statistic	32.41928
Two-Tail Test
Lower Critical Value	-1.65765
Upper Critical Value	1.657651
p-Value	3.32E-61
Reject the null hypothesis

For forming a 90% confidence interval for μ 1 − μ 2, the standard error is 2.066 ~2