Problem 2: A major keyboard manufacturer has a line of keyboards designed for apartment dwellers. These keyboards need to be light enough to be carried up ights of stairs. The lead engineer wants to use a new type of material. The engineer claims that the new keyboards will be lighter than the old keyboards. They take a sample of 4 keyboards manufactured using the old material and compute an average weight of 20 kg with a standard deviation of 1 kg. They take a sample of 7 keyboards manufactured using the new material and compute an average weight of 16 kg with a standard deviation of 2 kg. a] Conduct an appropriate hypothesis test using the critical value method. Use the old material as population 1. [Assume unequal population variances.) [9 marks] b] Explain what a Type ll Error means in this context. [1 mark] Problem 3: 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 rst, 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 -----_I_ DentistA -$120 $115 $110 -$105 $120 DentistB $140 $100 $130 $100 $95 $105 $100 $120 Conduct an appropriate hypothesis test using the critical value method. [10 marks]