Problem 1. the owner of a gasoline station wants to study gasoline

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:

1. State the null and alternative hypotheses.

2. What hypothesis test should you use? Circle one:

3. State your rejection rule (for the critical value approachmake sure to include your critical value(s)):

4. Calculate the test statistic (refer to part b).

5. 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. (7pts)

Critical value approach template:

1. State the null and alternative hypotheses.

2. What hypothesis test should you use? Circle one:

3. State your rejection rule (for the critical value approachmake sure to include your critical value(s)):

4. Calculate the test statistic (refer to part b).

5. 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? (1pt)
d. Refer to part (b). If you were using the p‐value approach, what would be the p‐value? (1pt)