Refer to Example 4. Workers in three occupations were questioned about satisfaction with their jobs. Suppose the number of responses in each of the four categories are

Assign 1 to very dissatisfied, 2 to a little dissatisfied, 3 to moderately satisfied, and 4 to very satisfied. (These data have means and proportions very satisfied similar to those reported in a recent large scale survey.)
(a) Calculate the sample mean and variance separately for firefighters and office supervisors. The scores for clergy have mean 3.79 and standard deviation .590.
(b) Construct a 95% confidence interval for the difference in mean satisfaction score for clergy and office supervisors.

Very A Linle Moder. Very DisDis ately Satis Sample Occupationsatisfied satisfed Satisfed fied Size Firefighters 6 Office Supervisors Clergy 24 180 226 85 149 247 78 90 12 6