Question

anufacturer claims that your new car gets 32 mpg on the highway. You suspect that the mpg is a different number for your car. The 52 trips on the highway that you took averaged 26.9 mpg and the standard deviation for these 52 trips was 12.6 mpg. What can be concluded at the a = 0.01 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: HO: ? Select an answer H: Select an answer y C. The test statistic (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is f: Based on this, we should Select an answer the null hypothesis. g. Thus, the final conclusion is that ... The data suggest that the population mean is not significantly different from 32 at a = 0.01, 50 there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is different from 32. The data suggest that the populaton mean is significantly different from 32 at a = 0.01, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is different from 32. The data suggest that the sample mean is not significantly different from 32 at a = 0.01, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is different from 26.9. h. Interpret the p-value in the context of the study. There is a 0.52178572% chance that the population mean mpg for your car on the highway is not equal to 32. If 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 a 0.52178572% chance that the sample mean for these 52 highway trips would either be less than 26.9 or greater than 37.1. If 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 a 0.52178572% chance that the population mean would either be less than 26.9 or greater than 37.1. There is a 0.52178572% chance of a Type I error. i. Interpret the level of significance in the context of the study.

Answer 1

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.

X

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

Ho: 32

H, :μ# 32

c) -

The test statistic: $T=\frac{\bar X-\mu}{s/\sqrt{n}}=\frac{26.9-32}{12.6/\sqrt{52}}=-2.91877=-2.919$

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[ |t₅₁| > 2.919 ] = 2P[ t₅₁> 2.919] = 0.0052

e) -

The p-value is smaller than $\alpha$

f) -

We reject H₀, at $\alpha$ level of significance if p-value<$\alpha$

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 different from 32 at $\alpha$ = 0.01, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is different from 32.

h) - Interpret the p-value

If 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 significance

If 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.

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