A manager is interested in determining the average hourly wage of individuals working at a branch of a major department store. She takes a random sample of 16 workers and calculates a mean of 22.52 and a standard deviation of 9.16. Assuming that the population distribution of hourly rates is normal, estimate with 90% confidence the mean hourly wage at the department store by answering the following questions.

i.What is the point estimator of this parameter and what is the sampling distribution of the standardised value of the point estimator. State and verify any required conditions.

Point estimator:

Standardised point estimator:

Sampling distribution of the standardised point estimator:

Is the required condition(s) satisfied? Why?