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, [tex]\bar d=-2.75[/tex].
The standard deviation of the differences is, [tex]S_{d}=4.268[/tex].
Compute the test statistic as follows:
[tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}=\frac{-2.75}{4.268/\sqrt{8}}=-1.82[/tex]
The degrees of freedom is, n - 1 = 7.
Compute the p-value as follows:
[tex]p-value=2\cdot P(t_{7}<-1.82)=0.112[/tex]
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.
