Question

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)**

- State and properly label the
**hypotheses**for this test.

- Find the
**critical value(s)**for this test.*(Sketching a graph is optional but recommended.)*

- Compute the
**test statistic***.**(Note: computing the P-value is optional.)*

**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]

- State the
**hypotheses**for this test and properly label them Ho and Ha.

- State the
**critical value(s)**for the test.*(Sketching a graph is optional but recommended.)*

- Compute the
**test statistic**for the test.

- Compute the
**P-value**for the test.

**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:

Answer #1

A car company says that the mean gas mileage for its luxury
sedan is at least 21 miles per gallon (mpg). You believe the claim
is incorrect and find that a random sample of 7 cars has a mean gas
mileage of 19 mpg and a standard deviation of 3 mpg. At alpha
equals 0.025, test the company's claim. Assume the population is
normally distributed. Which sampling distribution should be used
and why? State the appropriate hypothesis to test. What...

In a recent publication, it was reported that the average
highway gas mileage of tested models of a new car was 33.2 mpg and
approximately normally distributed. A consumer group conducts its
own tests on a simple random sample of 17 cars of this model and
finds that the mean gas mileage for their vehicles is 31.5 mpg with
a standard deviation of 3.5 mpg. Perform a test at the level to
determine if these data support the contention that...

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