How would you characterize the skewness of the distribution in Question 1—positively skewed, negatively skewed, or approximately normal? Provide a rationale for your answer.

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EXERCISE 26 Determining the Normality of a Distribution

1. Plot the frequency distribution for “Age at Enrollment” by hand or by using SPSS.

2. How would you characterize the skewness of the distribution in Question 1—positively skewed, negatively skewed, or approximately normal? Provide a rationale for your answer.

3. Compare the original skewness statistic and Shapiro-Wilk statistic with those of the smaller dataset (= 15) for the variable “Age at First Arrest.” How did the statistics change, and how would you explain these differences?

4. Plot the frequency distribution for “Years of Education” by hand or by using SPSS.

5. How would you characterize the kurtosis of the distribution in Question 4—leptokurtic, mesokurtic, or platykurtic? Provide a rationale for your answer.

6. What is the skewness statistic for “Age at Enrollment”? How would you characterize the magnitude of the skewness statistic for “Age at Enrollment”?

7. What is the kurtosis statistic for “Years of Education”? How would you characterize the magnitude of kurtosis for “Years of Education”?

8. Using SPSS, compute the Shapiro-Wilk statistic for “Number of Times Fired from Job.” What would you conclude from the results?

9. In the SPSS output table titled “Tests of Normality,” the Shapiro-Wilk statistic is reported along with the Kolmogorov-Smirnov statistic. Why is the Kolmogorov-Smirnov statistic inappropriate to report for these example data?

10. How would you explain the skewness statistic for a particular frequency distribution being low and the Shapiro-Wilk statistic still being significant at < 0.05?

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