## Question

###### Anufacturer claims that your new car gets 32 mpg on the highway. You suspect that the...

## Answers

Let the variable under interest is mpg for a car.

It is given that the sample of 52 strips on highway was taken resulted in the average = 26.9 mpg and standard deviation S = 12.6 mpg.

We want to check the manufacturer's claim that the new car gets 32 mpg on highway at level of significance = 0.01

a) -As the population standard deviation is not given we cannot use Z-test.

For this study, we should use

One-sample t-test.

b) -The null and alternative hypothesis would be

c) -The test statistic:

d) -Under null hypothesis, the test statistic T follows t-distribution with n-1=52-1=51 degrees of freedom

Also notice that this is two-sided test

P-value = P[ |t

_{51}| > 2.919 ] = 2P[ t_{51}> 2.919] =0.0052

e) -

The p-value is smaller than

f) -We reject H

_{0}, at level of significance if p-value<

Based on this, we should reject the null hypothesis.

g) -Thus, the final conclusion is that the data suggest that the population mean is

significantly differentfrom 32 at = 0.01, so there is statisticallysignificant evidenceto conclude that the population mean mpg for your car on the highway is different from 32.

h) -Interpret the p-valueIf the population mean mpg for you car on the highway is 32 and if you take another 52 strips on the highway, then there would be 0.52178572% chance that the sample mean for these 52 highway strips would either be less than 26.9 or greater than 37.1

i) -Interpret the level of significanceIf the population mean mpg for your car on the highway is 32 and if you take another 52 trips on the highway then there would be 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is different from 32.

I hope you find the solution helpful. If you have any doubt then feel free to ask in the comment section. Please do not forget to vote the answer. Thank you in advance!!!XWe were unable to transcribe this imageHo: 32H, :μ# 32We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image