Question

iven two dependent random samples with the following results: Population 1 70 60 72 55 69 50 55 74 Population 2 72 56 81 50 79 60 50 78 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 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Answer 1

The value of the test statistic is:

t = -1.112

Explanation:

In this case a paired difference test is to be performed.

The hypothesis can be defined as follows:

H₀: There is no difference between the two population means, i.e. d = 0.

Hₐ: There is a significant difference between the two population means, i.e. d ≠ 0.

The significance level of the test is, α = 0.10.

Use MS-Excel to perform the analysis.

Consider the output attached below.

The value of the test statistic is:

t = -1.112

The p-value of the two-tailed test is:

p-value = 0.303.

Decision rule:

Reject the null hypothesis if the p-value is less than the significance level.

p-value = 0.303 > α = 0.10.

The null hypothesis was failed to be rejected at 10% level of significance.

Conclusion:

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