Question

Given two dependent random samples with the following results:

Population 15666696660595654
Population 26564746463645460
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 the test.

Answer 1

The null hypothesis will not be rejected.

Explanation:

The hypothesis for the test is:

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.

Consider the Excel output attached.

The mean of the differences is,
`\bar d=-2.75`.

The standard deviation of the differences is,
`S_(d)=4.268`.

Compute the test statistic as follows:

`t=(\bar d)/(S_(d)/√(n))=(-2.75)/(4.268/√(8))=-1.82`

The degrees of freedom is, n - 1 = 7.

Compute the p-value as follows:

`p-value=2\cdot P(t_(7)<-1.82)=0.112`

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

p-value = 0.112 > α = 0.02.

The null hypothesis will not be rejected.