Past telephone companys records indicate that residential cu

Past telephone company’s records indicate that residential customers pay an average of $25.65 per month for long distance telephone calls. The company is interested in determining if this past average still applies to its current customers. If a random sample of 20 residential bills were taken, what shape would the sampling distribution of the mean for the desired test have?

A z-distribution regardless of the shape of the population.

A t-distribution regardless of the shape of the population.

A z-distribution if the population is appropriately normal.

A t-distribution if the population is appropriately normal.

Solution

A t-distribution if the population is appropriately normal.

Note that normality is definitely required. When sample sizes are large, CLT guarentees the normality of sampling distribution, but here sample size is small, and we need normality separately. Here we used t instead of z because population standard deviation was not known, and we will estimate it by sample standard deviation.