##### 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 |
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Q91 | N | Mean | Std. Deviation | Std. Error Mean | |

XR39AMT | 1 | 5204 | 11.8379 | 6.05181 | .08389 |

2 | 7036 | 11.1009 | 5.23526 | .06241 |

##### 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 |
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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 |

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 |
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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 |

(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 |
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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 |