Question

Given two dependent random samples with the following results:

Answer 1

Answer:

The null hypothesis will not be rejected.

Step-by-step 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:

$t=\frac{\bar d}{S_{d}/\sqrt{n}}=\frac{-2.75}{4.268/\sqrt{8}}=-1.82$

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

Compute the p-value as follows:

$p-value=2\cdot P(t_{7}$

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.