Question

In order to compare the means of two populations, independent random samples of 282 observations are selected from each population, with the following results:

Sample 1	Sample 2
x¯1=3	x¯2=4
s1=110	s2=200

(a)    Use a 97 % confidence interval to estimate the difference between the population means (?1−?2)(μ1−μ2).

_____ ≤(μ1−μ2)≤ ______
(b)    Test the null hypothesis: H0:(μ1−μ2)=0 versus the alternative hypothesis: Ha:(μ1−μ2)≠0. Using ?=0.03, give the following:

(i)    the test statistic z=

(ii)    the positive critical z score    

(iii)    the negative critical z score    

The final conclusion is

We can reject the null hypothesis (μ1−μ2)=0 in favor of the alternative (μ1−μ2)≠0.
There is not sufficient evidence to reject the null hypothesis (μ1−μ2)=0.

(c)    Test the null hypothesis: H0:(μ1−μ2)=23 versus the alternative hypothesis: Ha:(μ1−μ2)≠23. Using ?=0.03, give the following:

(i)    the test statistic z=

(ii)    the positive critical z score    

(iii)    the negative critical z score    

The final conclusion is

We can reject the null hypothesis (μ1−μ2)=23 in favor of the alternative (μ1−μ2)≠23.
There is not sufficient evidence to reject the null hypothesis (μ1−μ2)=23.

Answer 1