Suppose that job applicants applying for positions at a large corporation are required to complete a questionnaire to determine employment eligibility. Though many applicants do give acceptable responses to all 13 questions on the questionnaire, the human resources director suspects that recent job applicants are less likely to meet the minimum hiring requirements than past applicants.
To assess the recent pool of applicants, the director selects a simple random sample of 745 questionnaires and records the number of acceptable responses. She finds that this sample contains an average of 11.641 acceptable responses, with a standard deviation of 0.552 responses. Furthermore, records from all applications over the last several years give the standard deviation for the number of acceptable responses as 0.281.
The director uses this information to construct a 95%--confidence interval for the mean number of acceptable responses per questionnaire.
1. Does this situation meet the requirements for a z-confidence interval?
O No, because the number of acceptable answers on the pre-employment questionnaires is discrete and therefore cannot possibly be normally distributed in the population
O Yes, because the data come from a random sample.
O Yes, because the data come from a simple random sample, the population standard deviation is known, and the sample size is large.
O No, because the sample standard deviation is different from the standard deviation for all applicants.