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1.When students apply for graduate studies (i.e. at the master’sor doctoral level), they are
required to submit an official copy of their transcript, maileddirectly from the Registrar’s
Office at their academic institution. The customer service divisionof the Registrar’s
Office at a large Canadian university is interested in determiningif they are more than
25% faster at processing transcripts than another university in thearea, which can process
transcripts in 16 business hours. The customer service managerobtains a random sample
of 10 waiting times (in business hours), which are providedbelow.
11 12 18 20 23
15 10 12 13 14
a. Conduct an appropriate hypothesis test. Use the critical valuemethod. Use a
population standard deviation of 2 hours. [9 marks]
HINT: You will first have to determine what it means to be 25%faster, in terms
of hours.
b. Explain what a Type I Error means in this context. [1 mark]  
2. A major keyboard manufacturer has a line of keyboards designedfor apartment dwellers.
These keyboards need to be light enough to be carried up flights ofstairs. The lead
engineer wants to use a new type of material. The engineer claimsthat the new keyboards
will be lighter than the old keyboards.
They take a sample of 4 keyboards manufactured using the oldmaterial and compute an
average weight of 21 kg with a standard deviation of 1 kg.
They take a sample of 8 keyboards manufactured using the newmaterial and compute an
average weight of 17 kg with a standard deviation of 2 kg.
a. Conduct an appropriate hypothesis test using the p-value method.Use the old
material as population 1. [8 marks]
b. How much evidence is there against the null hypothesis in part(a)? [1 mark]
c. Explain what a Type II Error means in this context. [1 mark

3.An insurance company is interested in estimating thepopulation mean cost of basic dental
cleaning at dentists in Saskatoon. Suppose there are only twodentists in Saskatoon:
Dentist A and Dentist B. Suppose also that the cost of basic dentalcleaning varies only
depending on how well the patient practices regular dental hygiene,so that the cost of
basic dental cleaning roughly follows a Normal distributionregardless of the dentist.
The insurance company selects 8 sample patients and sends them toboth Dentist A and
Dentist B. They send the patients in random order, such that halfof the patients are seen
by Dentist A first, and half are seen by Dentist B first, so as notto bias the results. The
cost of basic dental cleaning for these 8 patients seen by bothDentists A and B are
provided below. The insurance company would like to determinewhether the population
mean cost of basic dental cleaning by Dentist A is different fromthe population mean
cost of basic dental care by Dentist B. Let the population of costsof basic dental care
from Dentist A be population 1.
Patient 1 2 3 4 5 6 7 8
Dentist A $100 $120 $125 $110 $95 $105 $120 $115
Dentist B $150 $100 $140 $100 $95 $105 $100 $120
Conduct an appropriate hypothesis test using the critical valuemethod. [10 marks]