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Paying for college College financial aid offices expect students to use summer earnings
Chapter 10, Problem 39(choose chapter or problem)
Paying for college College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this question by asking a random sample of 1296 students who had summer jobs how much they earned. The financial aid office separated the responses into two groups based on gender. Here are the data in summary form:30 Group n x sx Males 675 $1884.52 $1368.37 Females 621 $1360.39 $1037.46 (a) How can you tell from the summary statistics that the distribution of earnings in each group is strongly skewed to the right? The use of two-sample t procedures is still justified. Why? (b) Construct and interpret a 90% confidence interval for the difference between the mean summer earnings of male and female students at this university. (c) Interpret the 90% confidence level in the context of this study
Questions & Answers
QUESTION:
Paying for college College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this question by asking a random sample of 1296 students who had summer jobs how much they earned. The financial aid office separated the responses into two groups based on gender. Here are the data in summary form:30 Group n x sx Males 675 $1884.52 $1368.37 Females 621 $1360.39 $1037.46 (a) How can you tell from the summary statistics that the distribution of earnings in each group is strongly skewed to the right? The use of two-sample t procedures is still justified. Why? (b) Construct and interpret a 90% confidence interval for the difference between the mean summer earnings of male and female students at this university. (c) Interpret the 90% confidence level in the context of this study
ANSWER:Step 1 of 4
a) The distributions are skewed to the right because the earnings amounts cannot be negative, yet the standard deviation is almost as large as the distance between the mean and 0. The use of the two-sample t procedures is still justified because the t procedures are robust against Non-Normality in the populations with such large sample sizes.