Problem 1. The owner of a gasoline station wants to study gasoline purchasing habits by motorists at his station. He selects a random sample of 60 motorists during a certain week with the following results: the sample mean for purchases was 11.3 gallons, the sample standard deviation was 3.1 gallons, and 11 motorists purchased premium-grade gasoline. At the 0.10 level of significance (i.e., use α = .10),
a. Is there evidence that the population mean gasoline purchase was different from 10 gallons? Use the critical value approach. (7pts)
Critical value approach template:
State the null and alternative hypotheses.
What hypothesis test should you use? Circle one:
State your rejection rule (for the critical value approachmake sure to include your critical value(s)):
Calculate the test statistic (refer to part b).
State your conclusion based on (c) and (d). Circle one: Reject .
b. Is there evidence that fewer than 20% of all motorists at the station purchased premium-grade gasoline? Use the critical value approach.
Critical value approach template:
State the null and alternative hypotheses.
What hypothesis test should you use? Circle one:
State your rejection rule (for the critical value approachmake sure to include your critical value(s)):
Calculate the test statistic (refer to part b).
State your conclusion based on (c) and (d). Circle one: Do not reject .
c. Refer to part (b). If you were using the p-value approach, what would be the rejection rule?
d. Refer to part (b). If you were using the p-value approach, what would be the p-value?