Question

Compare the rape rate per 100,000 in those states that have executed a prisoner since 1976 to those that have not. Assume the alternative hypothesis is two-tailed with an alpha of 0.01. Executed a prisoner

Executed a prisoner	Have not executed a prisoner
36.8	92.5
33.3	18.7
33.1	29.2
28.2	25.9
41.6	38.3
43.2	27.1
39.5	27.9
25.7	54.1
37.2	41.2
32.9	33.2
27.8	15.3
25.6	19.7
41.1	23.8
24.7	46.9
37.4	46.3
24.4	19.5
26.8	16.4
28.5	21.9
39
50
25.4
40.1
42.7
34.2
28.8
44.4
35.7
36.2
37.9
24
46.7
27.1

a) What test do you run?

b) Provide the Excel or SPSS output.

c) What is your p-value?

d) What is your conclusion?

Answer 1

Here we are using Excel:

a) T- test , Two tail test, Assuming Unequal variance.

b) Excel output:

t-Test: Two-Sample Assuming Unequal Variances
	36.8	92.5
Mean	34.2968	29.7294
Variance	55.0617	138.4272
Observations	31	17
Hypothesized Mean Difference	0
df	23
t Stat	1.4502
P(T<=t) one-tail	0.0802
t Critical one-tail	2.4999
P(T<=t) two-tail	0.1605
t Critical two-tail	2.8073

c) P- value = 0.1605

d) Fail to reject the null hypothesis.

Here we have not sufficient evidence to reject the null hypothesis. We can't say that data differ from past data.