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Distribution Analysis
2. (4 points total) You have been hired as a consultant to determine if there appears to be a gender difference (variable Q91) in the hourly pay rates (variable XR39AMT) of recent college graduates. Using the Recent College Graduate Survey dataset, do the following:
(a) (1 point) Using descriptive statistics, describe the distributions of hourly pay rates separately for male recent college graduates and for female recent college graduates.
Ans: Both the distribution follows approximately a normal distribution.
(b) (1 point) Based only on your descriptive statistics from part a, does there appear to be a gender difference in the hourly pay rates of recent college graduates? Explain why or why not.
Ans: The output:

Group Statistics
  Q91 N Mean Std. Deviation Std. Error Mean
XR39AMT 1 5204 11.8379 6.05181 .08389
2 7036 11.1009 5.23526 .06241
There doesn’t appear to be a lot of difference as it seems very small.
Inferential Tests in SPSS
(c) (2 points) Conduct an inferential test in SPSS to determine whether the mean hourly pay rates differ between male and female recent college graduates. Indicate what type of inferential test you used to answer this question. Using conventional reporting standards, indicate what you conclude from these results. Be specific. [Note: Please copy and paste the SPSS output results in your response so that I can see the results that you obtained.]
Ans: Here we should use a two sample t-test.

Independent Samples Test
  Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference
Lower Upper
XR39AMT Equal variances assumed 33.172 .000 7.202 12238 .000 .73701 .10233 .53642 .93759
Equal variances not assumed     7.049 10237.174 .000 .73701 .10456 .53204 .94197
So, we can see that there is difference in the pays of male and female as the test is significant.
3. (4 points total) In a study several years ago, my Warner colleague, Brian Brent, and I found that urban schools spend a significantly greater share of their operating budgets on measures designed to promote school security (e.g., security guards, cameras, metal detectors, etc.) than non-urban schools. We did not consider, though, whether our finding was related to differences in the number of security-related incidents reported by urban versus non-urban schools.
Using the School Survey on Crime and Safety (SSOCS) dataset, do the following:
(a) (2 points) Conduct an inferential test to determine if the mean the number of incidents (variable INCID08) reported by urban schools differs from that of non-urban schools.
[Note that variable FR_URBAN in the dataset distinguishes schools by location type and they use the term “city” to denote urban schools.]
Indicate what type of inferential test you used to answer this question. Using conventional reporting standards, indicate what you conclude from these results. Be specific. [Again, please copy and paste the SPSS output results in your response so that I can see the results that you obtained.]
Ans: Here we are using the independent sample t-test. The output:

Independent Samples Test
  Levene's Test for Equality of Variances t-test for Equality of Means
F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference
Lower Upper
Total number of incidents recorded Equal variances assumed 64.382 .000 -8.791 2558 .000 -20.575 2.340 -25.164 -15.986
Equal variances not assumed     -7.631 954.694 .000 -20.575 2.696 -25.866 -15.284
The result is significant. Thus we can conclude that there is difference between the mean the number of incidents reported by urban schools and non-urban schools.
 (b) (2 points) Suppose that the true population mean for the number of incidents in urban schools is 60. Conduct an inferential test to determine whether the sample mean for the number of incidents (variable INCID08) for urban schools from the SSOCS dataset differs significantly from the population mean of 60. Indicate what type of inferential test you used to answer this question. Using conventional reporting standards, indicate what you conclude from these results. Be specific. [Again, please copy and paste the SPSS output results in your response so that I can see the results that you obtained.]
Ans: The output:

One-Sample Test
  Test Value = 60
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference
Lower Upper
Total number of incidents recorded -17.440 2559 .000 -18.286 -20.34 -16.23
The result is significant, thus there is a difference from the population mean.