Question

In: Statistics and Probability

A new car had been released for which the manufacturer reports that the car gets 23mpg...

A new car had been released for which the manufacturer reports that the car gets 23mpg for city driving. A consumer group feels that the true mileage is lower.

a) Perform the following hypothesis test, using α= .05. Assumptions: The gas mileage in the sample of 30 cars comes from an SRS drawn from the population of all mileage and the sample mean is 22.5 standard deviation is known, δ = 1.2.

b) State the type I and type II error in the context of the problem.

c) Calculate the power if in fact the average mileage of this new car is 21 mpg.

Expert Solution

a)

b)

Type I: It is the probability of rejecting the true null hypothesis. That is researcher incorrectly conclude that the true mileage is lower than 23 when it is 23 mpg.

Type II: It is the probability of fail to reject the false null hypothesis. That is researcher incorrectly conclude that the true mileage is not lower than 23 when it is lower than 23 mpg.

c)

The critical value of sample mean for which we will reject the null hypothesis is

Now z-score for and is

The power of the test is

power= P(z < 7.49) = 1.0000

orchestra answered 2 years ago

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