Exhibit 10.6. A university wants to compare out-of-state applicants\' mean SAT m
ID: 3357472 • Letter: E
Question
Exhibit 10.6.
A university wants to compare out-of-state applicants' mean SAT math scores (1) to in-state applicants' mean SAT math scores (2). The university looks at 35 in-state applicants and 35 out-of-state applicants. The mean SAT math score for in-state applicants was 540, with a standard deviation of 20. The mean SAT math score for out-of-state applicants was 555, with a standard deviation of 25. It is reasonable to assume the corresponding population standard deviations are equal.
Refer to Exhibit 10.6. At the 5% significance level, can the university conclude that the mean SAT math scores for in-state students and out-of-state students differ?
A) No, because the confidence interval contains zero
B) Yes, because the confidence interval contains zero
C) No, because the confidence interval does not contain zero
D) Yes, because the confidence interval does not contain zero
Explanation / Answer
The statistical software output for this problem is:
Two sample T summary confidence interval:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
(with pooled variances)
95% confidence interval results:
Hence,
We have sufficient evidence to conclude that the mean SAT math scores for in-state students and out-of-state students differ since the confidence interval does not contain zero.
Option D is correct.
Difference Sample Diff. Std. Err. DF L. Limit U. Limit 1 - 2 -15 5.4116277 68 -25.798735 -4.2012651Related Questions
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