Question

Use the given statistics to complete parts​ (a) and​ (b). Assume that the populations are normally distributed. ​(a) Test whether μ1>μ2 at the alphaαequals=0.01 level of significance for the given sample data.​ (b) Construct a 90​% confidence interval about μ1−μ2.			Population 1	Population 2
		n	24	23
		x overbarx	45.1	43.4
		s	5.8	12.7

Answer 1

To Test :-

H0 :-   μ1μ2

H1 :-   μ1>μ2

Test Statistic :-


t = 0.5861

Test Criteria :-
Reject null hypothesis if


DF = 30


Result :- Fail to Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 0.5861 ) = 0.2811
Reject null hypothesis if P value <    level of significance
P - value = 0.2811 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- We Accept H0

There is insufficient evidence to support the claim that μ1>μ2.

Confidence interval :-



Lower Limit =
Lower Limit = -3.2233
Upper Limit =
Upper Limit = 6.6233
90% Confidence interval is ( -3.2233 , 6.6233 )