In: Statistics and Probability
1. A criminologist is interested in whether there was any disparity in sentencing based on the race of the defendant. She selected two random samples of burglary convictions in one jurisdiction and recorded the prison terms given to the 10 white defendants in one sample and the 8 black defendants in the other sample. The sentence lengths (in years) for individuals in the two groups are shown below, along with the sample means and standard deviations. Using these data and a 0.05 alpha level, test the hypothesis that white and black defendants convicted of burglary in this jurisdiction receive prison sentences of different length.
White Defendants | Black Defendants |
---|---|
3 | 4 |
5 | 8 |
4 | 7 |
7 | 3 |
4 | 5 |
5 | 4 |
6 | 5 |
4 | 4 |
3 | |
2 |
a. In symbols and words, what is the null hypothesis for this test?
b. In symbols and words, what is the alternative hypothesis for this test?
c. Is this a one-sided or two-sided test? How do you know?
d. Will you use a z-test or a t-test in this situation? Why?
e. What is the critical value of the test statistic?
f. What is the value of the test statistic calculated from the sample results?
g. What decision about the null hypothesis does your test lead to?
h. Is the observed racial difference in sentence length statistically significant? Explain.
i. Would your decision be different if you used an alpha level of .01? Explain.