University of Chicago is concerned that the number of female students who take t

Question

University of Chicago is concerned that the number of female students who take technology-oriented classes. On average, each class has a female enrollment of 12, with a standard deviation of 5 (each class has a limit of 75 places, and usually fills up). As an attempt to remedy this situation, a mandatory workshop on the place of women in technology is built into New Student Week. Assume the n for your calculations is the number of classes listed below (16). Over the next year, the number of women who enroll in each computer science class open to freshmen is as follows: 31, 3, 13, 26, 16, 14, 27, 26, 18, 12, 22, 4, 10, 13, 8, 9 Give the 95% confidence interval for the mean for female enrollment in the year that the workshop was introduced (include a graph to locate the confidence interval).

Explanation / Answer

Solution:

sample mean=sum of observations/total obs

=252/16

=15.75

sample mean=15.75

sample sd=8.504901

n-1=16-1=15

alpha=1-0.95=0.05

alpha/2=0.05/2=0.025

t crit=2.131

95% confidence interval for mean is

sample mean-t crit(sample sd)/sqrt(n),sample mean+t crit(sample sd)/sqrt(n)

15.75-2.131*8.504901/sqrt(16),15.752.131*8.504901/sqrt(16)

11.219, 20.281

11.219<mu<20.281

lower limit=11

upper limit=20(rounding to nearest integer )

we are 95% confident that the true population mean lnumber of female students who take technology oriented classes ies in between 11 and 20.

x xbar x-xbar (x-xbar)^2 31 15.75 15.25 232.5625 3 15.75 -12.75 162.5625 13 15.75 -2.75 7.5625 26 15.75 10.25 105.0625 16 15.75 0.25 0.0625 14 15.75 -1.75 3.0625 27 15.75 11.25 126.5625 26 15.75 10.25 105.0625 18 15.75 2.25 5.0625 12 15.75 -3.75 14.0625 22 15.75 6.25 39.0625 4 15.75 -11.75 138.0625 10 15.75 -5.75 33.0625 13 15.75 -2.75 7.5625 8 15.75 -7.75 60.0625 9 15.75 -6.75 45.5625 1085 sample sd=sqrt(1085/16-1) samplesd=sqrt(1085/15) 8.504901

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