Question

# In order to compare the means of two populations, independent random samples of 282 observations are...

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.