In: Statistics and Probability
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.
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
Ha : 40.7
= 0.01
critical value for a two-tailed test is tc = 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.