Question

A. A sample of difference scores from a repeated-measures experiment has a mean difference of M_D = 3 with an estimated standard error of s_M = 1. If the sample size is n = 4, is this result sufficient to reject the null hypothesis, using a two-tailed test with alpha = .05?

B.

Hout, Duncan, and Sobel (1987) reported on the relative sexual satisfaction of heterosexual married couples. They asked each member of 91 couples to rate the degree to which they agreed with "Sex is fun for me and my partner," on a four-point scale ranging from 1 ("never or occasionally") to 4 ("almost always"). The mean difference was M_D = 0.0659 (women more satisfied), with SS = 152.

Why is it appropriate to use a related-samples t-test?

Group of answer choices

It is not appropriate-- a one-sample t-test should be used

It is not appropriate-- an independent samples t-test should be used

Because the subjects are matched in terms of the dependent variable

Because the satisfaction of the wife and the husband are not independent of each other

Answer 1

Part A) -

Given that M_D = 3 and Standard error S_M = 1

Sample size = n =4

Let be the true mean difference

Null hypothesis: H₀ : =0 versus Alternative hypothesis: H₁ : 0

Test statistic:

Under H₀ test statistic T follows t distribution with n-1 degrees of freedom.

We reject H₀ at 0.05 level of significance if

is such that

= 3.182

So,

Hence, there is no sufficient evidence to reject the null hypothesis at 0.05 level of significance.

Part B) -

The survey of relative sexual satisfaction of heterosexual married couple was conducted.

We know that related-samples t-test is used when the two samples produce paired data.

Hence, here in our context it is appropriate to use related-samples t-test

Because the subjects are matched in terms of the dependent variable and because the satisfaction of the wife and of the husband are not independent of each other.

#I suppose we are not expected to perform this test in this question

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