In order to compare the means of two populations, independent random samples of 397 observations are selected from each population, with the following results: Sample 1 Sample 2 x¯1=2 x¯2=0 s1=140 s2=145 (a) Use a 97 % confidence interval to estimate the difference between the population means (μ1−μ2). ____≤(μ1−μ2)≤____ (b) Test the null hypothesis: ?0:(?1−?2)=0 versus the alternative hypothesis: ??:(?1−?2)≠0. Using ?=0.03, give the following: (i) the test statistic ?= (ii) the positive critical z score (iii) the negative critical z score The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=0. B. We can reject the null hypothesis that (?1−?2)=0 and accept that (?1−?2)≠0. (c) Test the null hypothesis: ?0:(?1−?2)=21 versus the alternative hypothesis: ??:(?1−?2)≠21. Using ?=0.03, give the following: (i) the test statistic ?= (ii) the positive critical ? score (iii) the negative critical ? score The final conclustion is A. We can reject the null hypothesis that (?1−?2)=21 and accept that (?1−?2)≠21. B. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=21
In order to compare the means of two populations, independent random samples of 397 observations are selected from each population, with the following results:
| Sample 1 | Sample 2 |
| x¯1=2 | x¯2=0 |
| s1=140 | s2=145 |
(a) Use a 97 % confidence
____≤(μ1−μ2)≤____
(b) Test the null hypothesis: ?0:(?1−?2)=0 versus the alternative hypothesis: ??:(?1−?2)≠0. Using ?=0.03, give the following:
(i) the test statistic ?=
(ii) the positive critical z score
(iii) the negative critical z score
The final conclustion is
A. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=0.
B. We can reject the null hypothesis that (?1−?2)=0 and accept that (?1−?2)≠0.
(c) Test the null hypothesis: ?0:(?1−?2)=21 versus the alternative hypothesis: ??:(?1−?2)≠21. Using ?=0.03, give the following:
(i) the test statistic ?=
(ii) the positive critical ? score
(iii) the negative critical ? score
The final conclustion is
A. We can reject the null hypothesis that (?1−?2)=21 and accept that (?1−?2)≠21.
B. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=21.
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