Question

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 of the paired differences. Round your answer to one decimal place.

Step 3 of 5:

Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5:

Make the decision for the hypothesis test.

Answer #1

The statistical software output for this problem is:

Summary statistics:

Column | n | Mean | Variance | Std. dev. |
---|---|---|---|---|

Differences | 8 | -0.625 | 31.696429 | 5.6299581 |

Paired T hypothesis test:

μ_{D} = μ_{1} - μ_{2} : Mean of the
difference between Pop 1 and Pop 2

H_{0} : μ_{D} = 0

H_{A} : μ_{D} ≠ 0

**Hypothesis test results:**

Difference | Mean | Std. Err. | DF | T-Stat | P-value |
---|---|---|---|---|---|

Pop 1 - Pop 2 | -0.625 | 1.9904908 | 7 | -0.31399291 | 0.7627 |

Hence,

2) Standard deviation = **5.6**

3) Test statistic = -**0.314**

4) Decision rule: Reject Ho if |t| >
**2.998**

5) **Fail to Reject Null Hypothesis**

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.
Copy Data
Step 1 of 5:
State...

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
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
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.
Copy Data
Step 1 of 5 : ...

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 independent random samples with the following
results:
n1 = 226
^p1 = 0.55
n2 = 444
^p2 = 0.63
Can it be concluded that the proportion found in Population 2
exceeds the proportion found in Population 1? Use a
significance level of α=0.1 for the test.
Step 1 of 5: State the null and alternative hypotheses for the
test.
Step 2 of 5: Compute the weighted estimate of p, p‾. Round your
answer to three decimal places.
Step 3...

Given two independent random samples with the following
results:
n1=573, p^1=0.5
n2=454, pˆ2=0.6
Can it be concluded that the proportion found in Population 2
exceeds the proportion found in Population 1? Use a
significance level of α=0.1α=0.1for the test.
Step 1 of 5: State the null and alternative hypotheses for the
test.
Step 2 of 5: Compute the weighted estimate of p, p‾p‾. Round
your answer to three decimal places.
Step 3 of 5: Compute the value of the test statistic....

Given two dependent random samples with the following
results:Population 126484537404418Population 232363531383622Use this data to find the 90% confidence interval for the true
difference between the population means.Let d=(Population 1 entry)−(Population 2 entry). Assume that
both populations are normally distributed.Step 1 of 4: Find the mean of the paired differences, d‾. Round
your answer to one decimal place.Step 2 of 4: Find the critical value that should be used in
constructing the confidence interval. Round your answer to three
decimal places.Step...

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