The following matrix gives the correlations between ratings on pain made by 123 people suffering from extreme pain. The nine statements are 1. Whether or not I am in pain in the future depends on the...

The following matrix gives the correlations between ratings on pain made by 123 people suffering from extreme pain. The nine statements are

1. Whether or not I am in pain in the future depends on the skills of the doctors. 2. Whenever I am in pain, it is usually because of something I have done or not done3. Whether or not I am in pain depends on what the doctors do for me. 4. I cannot get any help for my pain unless I go to seek medical advice. 5. When I am in pain, I know that it is because I have not been taking proper exercise or eating the right food. 6. People’s pain results from their own carelessness. 7. I am directly responsible for my pain. 8. Relief from pain is chiefly controlled by the doctors. 9. People who are never in pain are just plain lucky. Each statement was scored on a scale from 1 (total agreement) to 6 (total disagreement).

Using the correlations between the first eight statements of the exercise, fit a correlated two-factor model in which questions 1, 3, 4, and 8 are assumed to be indicators of the latent variable Doctor’s Responsibility and questions 2, 5, 6, and 7 are assumed to be indicators of the latent variable Patient’s Responsibility. Find a 95% confidence interval for the correlation between the two latent variables