Question

In order to compare the means of two populations, independent random samples of 424 observations are selected from each population, with the following results:

Sample 1	Sample 2
x¯1=5169	x¯2=5417
s1=135	s2=130

Use a 96% confidence interval to estimate the difference between the population means (μ1−μ2).

? ≤(μ1−μ2)≤ ?

Test the null hypothesis: H0:(μ1−μ2)=0 versus the alternative hypothesis: Ha:(μ1−μ2)≠0. Using α=0.04, give the following:

the test statistic z =

postive critical z score =

negative critical z score =

The final conclustion is

A. There is not sufficient evidence to reject the null hypothesis that (μ1−μ2)=0.

or
B. We can reject the null hypothesis that (μ1−μ2)=0 and accept that (μ1−μ2)≠0.

Answer 1

Test Statistic :-


t = -27.2475

Test Criteria :-
Reject null hypothesis if | t | > t(α/2, DF)


DF = 844
t(α/2, DF) = t(0.04 /2, 844 ) = 2.057
| t | > t(α/2, DF) = 27.2475 > 2.057
Result :- Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 27.2475 ) = 0
Reject null hypothesis if P value < α = 0.04 level of significance
P - value = 0 < 0.04 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

Positive critical z score =2.057

Negative critical z score = -2.057

B. We can reject the null hypothesis that (μ1−μ2)=0 and accept that (μ1−μ2)≠0.

Confidence interval :-

t(α/2, DF) = t(0.04 /2, 844 ) = 2.057

Lower Limit =
Lower Limit = -266.7217
Upper Limit =
Upper Limit = -229.2783
96% Confidence interval is ( -266.7217 , -229.2783 )