In: Math
The table below summarizes the mean psychological distress score of persons who are married to or cohabiting with a romantic partner and those who are not. Psychological distress is a scale of feelings of depression and anxiety, ranging from 0 to 24, where higher scores indicate more distress. In answering these questions, show all of your work.
Mean |
Standard Deviation |
N |
|
Married/cohabiting |
4.25 |
4.04 |
831 |
Not in a relationship |
5.51 |
5.08 |
559 |
1. Construct a 95% confidence interval for psychological distress for respondents who are married to or cohabiting with a romantic partner.
2. Construct a 95% confidence interval for psychological distress for respondents who are not in a romantic relationship.
3. Compare the relative width of these two confidence intervals. Why do they differ?
4. Interpret one of these confidence intervals
5. Construct a 68% interval for respondents who are married to or cohabiting with a romantic partner.
1.
95% confidence interval for psychological distress for respondents who are married to or cohabiting with a romantic partner is (3.975, 4.525).
2.
95% confidence interval for psychological distress for respondents who are not in a romantic relationship is (5.088, 5.932).
3. Since the above two 95% CIs are completely disjoint so we are 95% confident that they are different.
4.
68% interval for respondents who are married to or cohabiting with a romantic partner is (4.1106,4.3894).