Question

 

In order to compare the means of two populations, independent random samples of 234 observations are selected from each population, with the following results:

Sample 1	Sample 2
x¯¯¯1=0x¯1=0	x¯¯¯2=4x¯2=4
s1=145s1=145	s2=100s2=100

(a)    Use a 99 % confidence interval to estimate the difference between the population means (μ1−μ2).

_______ ≤ (μ1−μ2) ≤ ________

(b)    Test the null hypothesis: H0:(μ1−μ2)=0 versus the alternative hypothesis: Ha:(μ1−μ2)≠0.

Using α=0.01α=0.01, give the following:

   the test statistic z=

The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that (μ1−μ2)=0.
B. We can reject the null hypothesis that (μ1−μ2)=0 and conclude that (μ1−μ2)≠0.

(c)    Test the null hypothesis: H0:(μ1−μ2)=22 versus the alternative hypothesis: Ha:(μ1−μ2)≠22. Using α=0.01, give the following:

   the test statistic z=

The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that (μ1−μ2)=22(μ1−μ2)=22.
B. We can reject the null hypothesis that (μ1−μ2)=22(μ1−μ2)=22 and conclude that (μ1−μ2)≠22(μ1−μ2)≠22.

Answer 1

(c)

Sample N Mean StDev SE Mean
1 234 0 145 9.5
2 234 4 100 6.5

Difference = μ (1) - μ (2)
Estimate for difference: -4.0
95% CI for difference: (-26.6, 18.6)
z-Test of difference = 22 (vs ≠): z-Value = -2.26 P-Value = 0.024 DF = 413

z value=-2.26

conclusion:

B. We can reject the null hypothesis that (μ1−μ2)=22(μ1−μ2)=22 and conclude that (μ1−μ2)≠22(μ1−μ2)≠22.