Find the rejection region for the standardized test statisti

Find the rejection region (for the standardized test statistic) for each hypothesis test based on the information given. The population is normally distributed. Identify the test as left-tailed, right-tailed, or two-tailed.

H0:=62 vs. Ha:62 @ =0.005, n = 8, unknown.

H0:=73 vs. Ha:>73 @ =0.001, n = 22, unknown.

Solution

H0:=62 vs. Ha:62 @ =0.005, n = 8, unknown is a two-tailed test, t=(xbar-)/(S/n)=(0+62)/(1/8)=175.3624, here t_cal value is more, so HO is rejected i.e.,Ha:62.

H0:=73 vs. Ha:>73 @ =0.001, n = 22, unknown is a right-tailed test, t=(xbar-)/(S/n)=(0-73)/(1/22)=342.4003, here t_cal value is more, so HO is rejected i.e.,Ha:>73.