Discussion:
Q1 An investigator for a consumer cooperative organized a study of the mileages obtainable from three different brands of gasoline. Using 15 identical motors set to run at the same speed, the investigator randomly assigned each brand of gasoline to 5 of the motors. Each of the motors was then run on 10 gallons of gasoline, with the total mileages obtained as follows.
Gas 1 Gas 2 Gas 3
220 244 252
251 235 272
226 232 250
246 242 238
260 225 256
Test the hypothesis that average mileage obtained is the same for all three types of gasoline. Use 5% level of significance.
Q2 During the first few weeks of the new television season, the evening news audience proportions were recorded as ABC- 31%, CBS- 34%, and NBC- 35%. A sample of 600 homes yielded the following viewing audience data.
Program #homes
ABC 150
CBS 200
NBC 250
Determine whether or not there has been a significant change in the number of viewing audience of the three networks.
a.State the null and alternative hypotheses to be tested.
b.Compute the expected frequencies.
c.Compute the test statistic.
d. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude?
e.Determine the p-value or its range and perform the test.