Question

A criminologist is interested in whether there was any disparity in sentencing based on the race of the defendant. She selected a random sample of 18 burglary convictions and recorded the prison terms given to the 10 white defendants and the 8 black defendants sampled. The sentence lengths (in years) for individuals in the two groups are shown below. Using these data and a .05 alpha level, test the null hypothesis that whites and blacks convicted of burglary in this jurisdiction do not differ with respect to prison sentence length.

White defendants		Black defendants
3		4
5		8
4		7
7		3
4		5
5		4
6		5
4		4
3
2

a.What is the null hypothesis for this test?

b.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.

j.If you increased the size of your sample by five times so that you had 50 white defendants and 40 black defendants, but the group means and variances remained the same, would you reach the same conclusion about the statistical significance of the racial difference in sentencing? Report the numbers used to make your decision.

Answer 1

Using Excel we get following output:

	t-Test: Two-Sample Assuming Equal Variances
		White defendants	Black defendants
	Mean	4.3	5
	Variance	2.233333333	2.857142857
	Observations	10	8
	Pooled Variance	2.50625
	Hypothesized Mean Difference	0
	df	16
	t Stat	-0.93216885
	P(T<=t) one-tail	0.182551579
	t Critical one-tail	1.745883669
	P(T<=t) two-tail	0.365103159
	t Critical two-tail	2.119905285

Steps Involve:

Copy data > Data > Data Analysis > t-test: Two Sample Assuming Equal Variance > ok > Variable 1 range (give/ select the range of white defendant) then variable 2 range (give/ select the range of black defendant) select alpha (1^st 0.05) give output range >ok.

Or we can find manually also