Suppose that we are interested in comparing the academic success of college students who belong to fraternal organizations and the academic success of those who do not belong to fraternal organizations. Random samples of size 40 are taken from each population where the variances and standard deviations are known. Sample Size Fraternity member (f): 40 Nonmembers (n): 40 Mean GPA Variance (2) 2.03 .46 2.21 .35 Construct a 96% confidence interval estimate for the difference between the mean GPAS (uf- un). Interpret this interval estimate. What can you conclude about the mean GPAs of the two groups?

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Suppose that we are interested in comparing the academic
success of college students who belong to fraternal organizations
and the academic success of those who do not belong to fraternal
organizations.
Random samples of size 40 are taken from each population where
the variances and standard deviations are known.
Sample Size Mean GPA Variance (2)
2.03
2.21
Fraternity member (f): 40
Nonmembers (n):
40
.46
.35
Construct a 96% confidence interval estimate for the difference
between the mean GPAS (uf- un).
Interpret this interval estimate. What can you conclude about the
mean GPAs of the two groups?
Transcribed Image Text:Suppose that we are interested in comparing the academic success of college students who belong to fraternal organizations and the academic success of those who do not belong to fraternal organizations. Random samples of size 40 are taken from each population where the variances and standard deviations are known. Sample Size Mean GPA Variance (2) 2.03 2.21 Fraternity member (f): 40 Nonmembers (n): 40 .46 .35 Construct a 96% confidence interval estimate for the difference between the mean GPAS (uf- un). Interpret this interval estimate. What can you conclude about the mean GPAs of the two groups?
Expert Solution
Step 1: Given Information:

Fraternity member:

Sample size n subscript 1 equals 40

Sample mean x with bar on top subscript 1 equals 2.03

Population variance sigma squared subscript 1 equals 0.46

Nonmembers:

Sample size n subscript 2 equals 40

Sample mean x with bar on top subscript 3 equals 2.21

Population variance sigma subscript 2 squared equals 0.35

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