Consider a situation to test H 0 : ?1??2=0?1??2=0, H a : ?1??2?0?1??2?0, where ?
ID: 2909797 • Letter: C
Question
Consider a situation to test H0: ?1??2=0?1??2=0, Ha: ?1??2?0?1??2?0, where ?1?1 and ?2?2 are the means of two populations, Group 1 and Group 2. Two random samples of 15 and 12 observations are selected from Groups 1 and 2, respectively. The following table shows the two-sample t test results at ?? = 5% assuming equal population variances:
Step 1:
Based on the above results, we conclude at ?? = 5% that
?1?1 is different from ?2?2 because the P-value is 0.080.
?1?1 is not significantly different from ?2?2 because the P-value is 0.080.
?1?1 is different from ?2?2 because the P-value is 0.040.
?1?1 is not significantly different from ?2?2 because the P-value is 0.040.
Step 2:
The degrees of freedom of the above test statistic are
Step 3:
A point estimate for the difference between the two population means, ?1??2?1??2, is (Round your answer to the nearest whole number.)
Step 4:
The standard error of the difference between the two sample means is (Give your answer to 3 decimal places.)
?1?1 is different from ?2?2 because the P-value is 0.080.
?1?1 is not significantly different from ?2?2 because the P-value is 0.080.
?1?1 is different from ?2?2 because the P-value is 0.040.
?1?1 is not significantly different from ?2?2 because the P-value is 0.040.
Step 2:
The degrees of freedom of the above test statistic are
Step 3:
A point estimate for the difference between the two population means, ?1??2?1??2, is (Round your answer to the nearest whole number.)
Step 4:
The standard error of the difference between the two sample means is (Give your answer to 3 decimal places.)
Explanation / Answer
1)
?1 is not significantly different from ?2 because the P-value is 0.080.
2)degrees of freedom of the above test statistic are =15+12-2=25
3)estimate for the difference between the two population means =35-31 =4
4)
standard error of the difference between the two sample means is =sqrt(Sp2*(1/n1+1/n2))
=sqrt(120*(1/15+1/12)=4.243