Respuesta :
Answer:
The mean difference in the husband's versus the wife's satisfaction level is negative.
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
In this case a paired t-test is used to determine if the mean difference in the husband's versus the wife's satisfaction level is negative .
The hypothesis for the test can be defined as follows:
H₀: The mean difference in the husband's versus the wife's satisfaction level is not negative, i.e. d ≥ 0.
Hₐ: The mean difference in the husband's versus the wife's satisfaction level is negative, i.e. d < 0.
The information computed from the provided data is:
[tex]n=10\\\bar d=0.50\\s_{d}=0.8498[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar d}{s_{d}/\sqrt{n}}=\frac{0.50}{0.8498/\sqrt{10}}=1.86[/tex]
The test statistic value is 1.86.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
The degrees of freedom is:
df = n - 1
= 10 - 1
= 9
Compute the p-value of the test as follows:
[tex]p-value=P(t_{9}<1.86)=0.048[/tex]
*Use a t-table.
The p-value of the test is 0.048.
p-value= 0.048 > α = 0.05
The null hypothesis was rejected at 5% level of significance.
Thus, it can be concluded that the mean difference in the husband's versus the wife's satisfaction level is negative.

