A professor is interested in comparing the average amount spent on textbooks for

Question

A professor is interested in comparing the average amount spent on textbooks for freshmen and sophomores. A random sample of 15 freshmen yielded a sample mean amount of $1016 and a sample standard deviation of $54. A random sample of 12 sophomores yielded a sample mean amount of $1236 and a sample standard deviation of $320. Construct a 95% confidence interval for the difference between the mean amount spent on textbooks hy 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 freedorm in this case? Give your answer to four decimal places. 11.5022 b) What is the lower confidence limit on the interval? Give your answer to two decimal places. c) What is the upper confidence limit on the interval? Give your answer to two decimal places. d) Using this interval, is it reasonable to conclude that the average sophomore spends more than the average freshman? because the interval contains 0 No because the Interval contalns 0 Yes because the upper endpurt on the interval is below 0. Yes because the upper endpoint on the interval 15 above 0

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,

95% confidence interval will be:

Lower confidence limit = -424.53

Upper confidence limite = -15.47

Difference Sample Diff. Std. Err. DF L. Limit U. Limit 1 - 2 -220 93.422339 11.502206 -424.53112 -15.468877

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