A public utility is conducting a survey of mechanical engineers to learn more about the factors influencing the choice of heating, ventilation, and air conditioning (HVAC) equipment for new commercial buildings. A total of 120 firms in the utility's service area are engaged in designing HVAC systems. The sampling plan is to use cluster sampling with each firm representing a cluster. For each firm in the sample, all of the mechanical engineers will be interviewed. Approximately 500 mechanical engineers are believed to be employed by the 120 firms. A sample of 10 firms was taken. Among other things, the age of each respondent was recorded as well as whether the respondent had attended the local university.

a. Estimate the mean age of mechanical engineers engaged in this type of work.
b. Estimate the proportion of mechanical engineers in the utility's service area who attended the local university.
c. Develop an approximate 95% confidence interval for the mean age of mechanical engineers designing HVAC systems for commercial buildings.
d. Develop an approximate 95% confidence interval for the proportion of mechanical engineers in the utility's service area who attended the local university.

Transcribed Image Text:

Total of Respondents' Ages 520 Number Attending Local University Cluster (i) 12 4 29 270 129 102 48 337 462 12 35 10 Totals 50