Question

Given two dependent random samples with the following results:

Population 1 | 70 | 69 | 60 | 60 | 59 | 54 | 62 | 68 |
---|---|---|---|---|---|---|---|---|

Population 2 | 79 | 59 | 66 | 52 | 66 | 59 | 55 | 70 |

Can it be concluded, from this data, that there is a significant difference between the two population means?

Let d=(Population 1 entry)−(Population 2 entry)d=(Population 1 entry)−(Population 2 entry). Use a significance level of α=0.02α=0.02 for the test. Assume that both populations are normally distributed.

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Step 1 of 5 :

State the null and alternative hypotheses for the test.

Step 2 of 5:

Find the value of the standard deviation of the paired differences.

Step 3 of 5:

Compute the value of the test statistic.

Step 4 of 5

Determine the decision rule for rejecting the null hypothesis Ho. Round to three decimals

Step 5 of 5

Make the decision for the hypothesis test

Answer #1

To Test :-

H0 :-

H1 :-

Test Statistic :-

t = -0.1857

Test Criteria :-

Reject null hypothesis if

**Result :- Fail to reject null hypothesis**

Decision based on P value

P - value = P ( t > 0.1857 ) = 0.8579

Reject null hypothesis if P value <
level of significance

P - value = 0.8579 > 0.02 ,hence we fail to reject null
hypothesis

**Conclusion :- Fail to reject null
hypothesis**

There is not sufficient evidence to support the claim that there is a difference between the two population mean.

Given two dependent random samples with the following
results:
Population 1
59
57
77
60
59
64
72
67
Population 2
61
53
84
53
69
74
64
73
Can it be concluded, from this data, that there is a significant
difference between the two population means?
Let d=(Population 1 entry)−(Population 2 entry)d=(Population 1
entry)−(Population 2 entry). Use a significance level of
α=0.01α=0.01 for the test. Assume that both populations are
normally distributed.
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Step 1 of 5:
State...

Given two dependent random samples with the following
results:
Population 1: 60 74 66 73 68 69 81 67
Population 2: 69 70 75 68 71 71 72 69
Can it be concluded, from this data, that there is a significant
difference between the two population means? Let d=(Population 1
entry)−(Population 2 entry). Use a significance level of α=0.02 for
the test. Assume that both populations are normally
distributed.
Step 1 of 5: State the null and alternative hypotheses for...

Given two dependent random samples with the following
results:
Population 1
69
55
53
56
59
74
76
71
Population 2
75
53
58
53
64
77
72
77
Can it be concluded, from this data, that there is a significant
difference between the two population means?
Let d=(Population 1 entry)−(Population 2 entry)d=(Population 1
entry)−(Population 2 entry). Use a significance level of
α=0.02 for the test. Assume that both populations are
normally distributed.
Step 1 of 5: State the null and...

Given two dependent random samples with the following
results:
Population 1
56
66
69
66
60
59
56
54
Population 2
65
64
74
64
63
64
54
60
Can it be concluded, from this data, that there is a significant
difference between the two population means?
Let d=(Population 1 entry)−(Population 2 entry)d=(Population 1
entry)−(Population 2 entry). Use a significance level of
α=0.02α=0.02 for the test. Assume that both populations are
normally distributed.

Given two dependent random samples with the following
results:
Population 1
58
76
77
70
62
76
67
76
Population 2
64
69
83
60
66
84
60
81
Can it be concluded, from this data, that there is a significant
difference between the two population means?
Let d=(Population 1 entry)−(Population 2 entry). Use a
significance level of α=0.01 for the test. Assume that both
populations are normally distributed.
Step 1 of 5: State the null and alternative hypotheses for...

Given two dependent random samples with the following
results:
Population 1
81
59
57
84
52
62
65
80
Population 2
85
53
66
82
54
64
57
84
Can it be concluded, from this data, that there is a significant
difference between the two population means?
Let d=(Population 1 entry)−(Population 2 entry). Use a
significance level of α=0.02 for the test. Assume that both
populations are normally distributed.
Step 2 of 5:
Find the value of the standard deviation...

Given two dependent random samples with the following
results:
Population 1
54
83
68
66
62
60
70
62
Population 2
59
74
76
64
64
69
67
64
Can it be concluded, from this data, that there is a significant
difference between the two population means?
Let d=(Population 1 entry)−(Population 2 entry) . Use a
significance level of α=0.01 for the test. Assume that both
populations are normally distributed.
Step 1 of 5:
State the null and alternative hypotheses...

Given two dependent random samples with the following
results:
Population 1
62
60
71
67
63
64
80
65
Population 2
64
54
79
62
72
72
73
75
Can it be concluded, from this data, that there is a significant
difference between the two population means?
Let d=(Population 1 entry)−(Population 2 entry). Use a
significance level of α=0.1 for the test. Assume that both
populations are normally distributed.
Step 1 of 5: State the null and alternative hypotheses for...

Given two dependent random samples with the following
results:
Population 1
77
64
60
71
56
56
62
55
Population 2
84
54
68
61
60
63
60
63
Can it be concluded, from this data, that there is a significant
difference between the two population means?
Let d=(Population 1 entry)−(Population 2 entry)d=(Population 1
entry)−(Population 2 entry). Use a significance level of α=0.1α=0.1
for the test. Assume that both populations are normally
distributed.
Step 3 of 5 : Compute the value...

Given two dependent random samples with the following
results:
Population 1
6060
7474
6666
7373
6868
6969
8181
6767
Population 2
6969
7070
7575
6868
7171
7171
7272
6969
Can it be concluded, from this data, that there is a significant
difference between the two population means?
Let d=(Population 1 entry)−(Population 2 entry)d=(Population 1
entry)−(Population 2 entry). Use a significance level of
α=0.02α=0.02 for the test. Assume that both populations are
normally distributed.
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Step 1 of 5 : ...

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