Question

1. Conduct an independent sample t-test (alpha= .05) in Excel to determine whether there is a significant difference in the age of offenders at prison admissions between White and Black offenders. For this t-test, assume that the variances of the two groups are equal. In your summary, please discuss the null hypothesis, alternative hypothesis, the result of this hypothesis test, and interpret the result.

t-Test: Two-Sample Assuming Equal Variances
	White	Black
Mean	235.5714286	199.164557
Variance	44025.35714	87049.21616
Observations	21	79
Pooled Variance	78268.83677
Hypothesized Mean Difference	0
df	98
t Stat	0.530044235
P(T<=t) one-tail	0.298640076
t Critical one-tail	1.660551217
P(T<=t) two-tail	0.597280151
t Critical two-tail	1.984467455

Answer 1

From provided information,

The following null and alternative hypothesis need to tested.

Ho : There is no difference in age of offenders at prison admission between White and Black offenders.

I.e.   

Ha : Therw is difference i age of offenders at prison admission between White and Black offenders.

I.e.   

Therefore this is a two tailed test.

Given output of t test :

P- value for two tailed test = 0.5973

Decision : Do not reject Ho, because p- value is greater than 0.05 level of significance.

Conclusion :There is not a significant difference in the age of offenders at prison admissions between White and Black offenders at 0.05 level of significance.

Thank You!