13. 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: Group Males Females n 675 621 X $1884.52 $1360.39 Sx $1368.37 $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? A graph of the data reveals no outliers. The use of two-sample 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.

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13. 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:
Group
Males
Females
n
675
621
x
$1884.52
$1360.39
€
HI
Sx
$1368.37
$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? A graph of the data reveals no outliers. The use of
two-sample 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.
Transcribed Image Text:13. 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: Group Males Females n 675 621 x $1884.52 $1360.39 € HI Sx $1368.37 $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? A graph of the data reveals no outliers. The use of two-sample 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.
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