Question

# 5. A consumer watchdog group tests the gas mileage for a specific model of car using...

5. A consumer watchdog group tests the gas mileage for a specific model of car using a (random) sample of 14 cars.

This sample has a mean gas mileage of 27.6 mpg and a standard deviation of 3.2 mpg.

(a) Find a 99% confidence interval for the mean gas mileage of all cars of this model.                                  [8 pts]

(b) Complete each step below to perform a (traditional) hypothesis test to test the claim in bold made by the car manufacturer. (Use a 5% significance level.)                                                                                       [3 pts each part]

Claim: The mean gas mileage for this vehicle model exceeds 26.0 miles per gallon (mpg)

1. State and properly label the hypotheses for this test.
1. Find the critical value(s) for this test.   (Sketching a graph is optional but recommended.)
1. Compute the test statistic.               (Note: computing the P-value is optional.)
1. State your conclusion by first choosing one of the following:      Reject Ho   - or -   Fail to reject Ho

Then interpret this conclusion in the context of the original claim by writing a sentence in “plain English”:

6. A botanist has produced a new variety of hybrid wheat that is supposedly better able to withstand drought conditions. It is known that the parent plants for this hybrid wheat have 80% of their seeds germinate.

The botanist makes this claim: the new hybrid seeds have the same germination rate as the parent plants (meaning the same proportion of the new hybrid seeds will germinate).

Suppose a sample of 400 seeds for the hybrid wheat were tested and 312 of them germinated.

Use this sample data to test the claim in bold above at the 5% significance level by completing parts (a) – (e) below:                                                                                                                                       [3 pts each part]

1. State the hypotheses for this test and properly label them Ho and Ha.
1. State the critical value(s) for the test.    (Sketching a graph is optional but recommended.)
1. Compute the test statistic for the test.
1. Compute the P-value for the test.
1. State your conclusion by first choosing one of the following:      Reject Ho    - or -    Fail to reject Ho

Then interpret this conclusion in the context of the original claim by writing a sentence in “plain English” below: