4. 2/4 points| Previous Answers My N A professor is interested in comparing the

Question

4. 2/4 points| Previous Answers My N A professor is interested in comparing the average amount spent on textbooks for freshmen and sophomores. A random sample of 10 freshmen yielded a sample mean amount of $1040 and a sample standard deviation of $51. A random sample of 8 sophomores yielded a sample mean amount of $1274 and a sample standard deviation of $349. Construct a 95% confidence interval for the difference between the mean amount spent on textbooks by freshmen and the mean amount spent by sophomores (ie. do freshmen minus sophomores). Since the sample standard deviations are wildly different, use a method which does not assume the populations have the same variance. Assume normality. a) what is the appropriate degrees of freedom in this case? Give your answer to four decimal places. 7.2396 b) What is the lower confidence limit on the interval? Give your answer to two decimal places. -528.25 c) What is the upper confidence limit on the interval? Give your answer to two decimal places. 60.25

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
(without pooled variances)

95% confidence interval results:

Hence,

a) Degrees of freedom = 7.2396

b) Lower confidence interval = -526.29

c) Upper confidence interval = 58.29

Difference Sample Diff. Std. Err. DF L. Limit U. Limit 1 - 2 -234 124.43964 7.2395701 -526.29052 58.290519

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