Question

1. ) Computers in some vehicles calculate various quantities related to performance.  One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg).  For one vehicle equipped in this way, the car was set to 60 miles per hour by cruise control, and the mpg were recorded at random times.  Here are the mpg values from the experiment:

37.2     21.0     17.4     24.9     27.0     36.9     38.8     35.3     32.3     23.9

19.0     26.1     25.8     41.1     34.4     32.5     25.3     26.5     28.2     22.1

The vehicle sticker information for the vehicle states a highway average of 27 mpg.  Perform a hypothesis test at 5% significance level to determine if the results of this experiment are consistent with the vehicle sticker.

1. (30 points) Give the hypotheses, test statistic, rejection region, p-value, decision, and interpretation.
2. (5 points) What would a Type II error be in this situation?

Answer 1

a)

Since we fail to reject the null hypothesis, we have evidence that the results of this experiment are consistent with the vehicle sticker.

b)

A type II error is a statistical term referring to the non-rejection of a false null hypothesis.

Here type II error means that the result of the experiment are not consistent with the vehicle sticker but we have concluded that it is consistent with the vehicle sticker