Problem: An insurance company is interested in estimating the population mean cost of basic dental cleaning at dentists in a Saskatoon neighborhood. Suppose there are only two dentists in the neighborhood: Dentist A and Dentist B. Suppose also that the cost of basic dental cleaning varies only depending on how well the patient practices regular dental hygiene, so that the cost of basic dental cleaning roughly follows a Normal distribution regardless of the dentist.

The insurance company selects 8 sample patients and sends them to both Dentist A and Dentist B. They send the patients in random order, such that half of the patients are seen by Dentist A first, and half are seen by Dentist B first, so as not to bias the results. The cost of basic dental cleaning for these 8 patients seen by both Dentists A and B are provided below. The insurance company would like to determine whether the cost of basic dental cleaning by Dentist A is different from the cost of basic dental care by Dentist B on average. Let the population of costs of basic dental care from Dentist A be population 1.

Patient 1 2 3 4 5 6 7 8

Dentist A $110 $120 $115 $110 $90 $105 $120 $115

Dentist B $140 $100 $130 $100 $95 $105 $100 $120

Conduct an appropriate hypothesis test using the critical value method.