Question

Complete a 6-step hypothesis test using the following scenario:

In 2012, the mean age of an inmate on death row was 40.7 years, according to data from the U.S. Department of Justice. A sociologist wondered whether the mean age of a death row inmate has changed since then. She randomly selects 32 death row inmates and finds that their mean age is 38.9 with a standard deviation of 9.6. Test using a 0.01 significance level.

Answer 1

Solution :

= 40.7

= 38.9

S = 9.6

n = 32

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 40.7

H_a :    40.7

= 0.01

critical value for a two-tailed test is t_c = 2.744

Test statistic = t

= ( - ) / S / n

= (38.9-40.7) /9.6 / 32

= -1.061

P(z <-1.061 ) = 0.297

P-value = 0.297

=0.01

p = 0.297 ≥ 0.01, it is concluded that the null hypothesis is not rejected.

There is not enough evidence to claim that the population mean \muμ is different than 40.7, at the 0.01 significance level.