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A group of researchers want to determine if there are any significant differences in marital satisfaction...

A group of researchers want to determine if there are any significant differences in marital satisfaction between male and female spouses. To test this hypothesis, they collected data on marital satisfaction from 28 couples (i.e., 28 men and 28 women). They observed that the average marital satisfaction among men was 6.5, and the average among women was 6.0. The sum of squares for the difference scores (SSD) was 440. Additionally, male and female spouse marital satisfaction were strongly related (r = .51). Use a confidence interval (where α = .01) to determine if there is a significant difference in marital satisfaction between male and female spouses.

      15.  Identify the alternative hypothesis

      16.  List your estimated standard error

      17.  List the t-value used to construct your confidence interval

      18.  List the lower bound of your confidence interval (where: Men - Women)

      19.  List the upper bound of your confidence interval (where: Men - Women)

      20.  Is the difference in marital satisfaction between male and female spouses statistically significant? (Yes/No)

      21.  Calculate Cohen’s d for the difference in marital satisfaction

      22.  Determine the t value for the correlation between spousal life satisfaction

Math   Statistics-And-Probability   
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Answer #1

(15) d-bar ≠ 0

(16) Variance = 440/27 = 16.296, so s = 4.037

Standard error = s/√n = 4.037/√28 = 0.7629

(17) Critical t- score for df = 27 and 99% confidence is t = 2.7707

d-bar = 6.5 - 6 = 0.5

Width of the confidence interval = t * SE = 2.113813004

(18) Lower limit of the confidence interval = d-bar - width = -1.613813004

(19) Upper limit of the confidence interval = d-bar + width = 2.613813004

(20) The above confidence interval includes 0. So we conclude that there is no significant difference between men and women

(21) Cohen's d = d-bar/s = 0.5/4.037 = 0.124

(22) df = 26

SE = √{(1 - r^2)/df} =   √((1 - 0.51^2)/26) = 0.168694079

t = r/SE = 0.51/0.168694079053452 = 3.023224068

Critical t- score = 2.7787

[Please give me a Thumbs Up if you are satisfied with my answer. If you are not, please comment on it, so I can edit the answer. Thanks.]

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