The null hypothesis is H0​: μ1=μ2 and the alternative hypothesis is as specified. The provided data are from a simple random paired sample from the two populations under consideration. Use the paired​ t-test to perform the required hypothesis test at the​ 10% significance level. Ha​: μ1≠μ2   Observations from Pair Population 1 Population 2   1 23 21   2 7 6   3 24 21   4 14 8   5 12 8   6 5 6   7 16 13     Find the test statistic. Use population 1−population 2 as the difference.   t=____________ ​(Round to three decimal places as​ needed.)   Find the critical​ value(s).   The critical​ value(s) is/are ____________ ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)   What is the correct conclusion for the hypothesis​ test?   A. Reject H0. There is sufficient evidence that μ1≠μ2.   B. Do not reject H0. There is not sufficient evidence that μ1≠μ2.   C. Reject H0. There is not sufficient evidence that μ1≠μ2.   D. Do not reject H0. There is sufficient evidence that μ1≠μ2.

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The null hypothesis is
H0​: μ1=μ2
and the alternative hypothesis is as specified. The provided data are from a simple random paired sample from the two populations under consideration. Use the paired​ t-test to perform the required hypothesis test at the​ 10% significance level.
Ha​: μ1≠μ2
 
Observations from
Pair
Population 1
Population 2
 
1
23
21
 
2
7
6
 
3
24
21
 
4
14
8
 
5
12
8
 
6
5
6
 
7
16
13
 

 

Find the test statistic. Use population 1−population 2 as the difference.
 
t=____________
​(Round to three decimal places as​ needed.)
 
Find the critical​ value(s).
 
The critical​ value(s) is/are ____________
​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)
 
What is the correct conclusion for the hypothesis​ test?
 
A. Reject H0. There is sufficient evidence that μ1≠μ2.
 
B. Do not reject H0. There is not sufficient evidence that μ1≠μ2.
 
C. Reject H0. There is not sufficient evidence that μ1≠μ2.
 
D. Do not reject H0. There is sufficient evidence that μ1≠μ2.
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