The manufacturer claims that your new car gets 26 mpg on the highway. You suspect that the mpg is a different number for your car. The 43 trips on the highway that you took averaged 24.5 mpg and the standard deviation for these 43 trips was 2.8 mpg. What can be concluded at the α = 0.10 level of significance?

For this study, we should use Select an answer z-test for a population proportion t-test for a population mean

The null and alternative hypotheses would be:

H0:H0:  ? p μ  Select an answer = ≠ > <

H1:H1:  ? μ p  Select an answer ≠ = < >

The test statistic ? z t  =  (please show your answer to 3 decimal places.)

The p-value =  (Please show your answer to 4 decimal places.)

The p-value is ? > ≤  αα

Based on this, we should Select an answer fail to reject accept reject  the null hypothesis.

Thus, the final conclusion is that ...

The data suggest that the sample mean is not significantly different from 26 at αα = 0.10, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is different from 24.5.

The data suggest that the populaton mean is significantly different from 26 at αα = 0.10, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is different from 26.

The data suggest that the population mean is not significantly different from 26 at αα = 0.10, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is different from 26.

Interpret the p-value in the context of the study.

There is a 0.10748402% chance that the population mean mpg for your car on the highway is not equal to 26.

If the population mean mpg for your car on the highway is 26 and if you take another 43 trips on the highway then there would be a 0.10748402% chance that the population mean would either be less than 24.5 or greater than 27.5.

If the population mean mpg for your car on the highway is 26 and if you take another 43 trips on the highway, then there would be a 0.10748402% chance that the sample mean for these 43 highway trips would either be less than 24.5 or greater than 27.5.

There is a 0.10748402% chance of a Type I error.

Interpret the level of significance in the context of the study.

There is a 10% chance that the population mean mpg for your car on the highway is different from 26.

If the population population mean mpg for your car on the highway is different from 26 and if you take another 43 trips on the highway, then there would be a 10% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is equal to 26.

There is a 10% chance that you own an electric powered car, so none of this matters to you anyway.

If the population mean mpg for your car on the highway is 26 and if you take another 43 trips on the highway, then there would be a 10% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is different from 26.

Question

The manufacturer claims that your new car gets 26 mpg on the highway. You suspect that the mpg is a different number for your car. The 43 trips on the highway that you took averaged 24.5 mpg and the standard deviation for these 43 trips was 2.8 mpg. What can be concluded at the α = 0.10 level of significance?

For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
The null and alternative hypotheses would be:

H0:H0: ? p μ Select an answer = ≠ > <

H1:H1: ? μ p Select an answer ≠ = < >

The test statistic ? z t = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)
The p-value is ? > ≤ αα
Based on this, we should Select an answer fail to reject accept reject the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest that the sample mean is not significantly different from 26 at αα = 0.10, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is different from 24.5.
- The data suggest that the populaton mean is significantly different from 26 at αα = 0.10, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is different from 26.
- The data suggest that the population mean is not significantly different from 26 at αα = 0.10, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is different from 26.
Interpret the p-value in the context of the study.
- There is a 0.10748402% chance that the population mean mpg for your car on the highway is not equal to 26.
- If the population mean mpg for your car on the highway is 26 and if you take another 43 trips on the highway then there would be a 0.10748402% chance that the population mean would either be less than 24.5 or greater than 27.5.
- If the population mean mpg for your car on the highway is 26 and if you take another 43 trips on the highway, then there would be a 0.10748402% chance that the sample mean for these 43 highway trips would either be less than 24.5 or greater than 27.5.
- There is a 0.10748402% chance of a Type I error.
Interpret the level of significance in the context of the study.
- There is a 10% chance that the population mean mpg for your car on the highway is different from 26.
- If the population population mean mpg for your car on the highway is different from 26 and if you take another 43 trips on the highway, then there would be a 10% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is equal to 26.
- There is a 10% chance that you own an electric powered car, so none of this matters to you anyway.
- If the population mean mpg for your car on the highway is 26 and if you take another 43 trips on the highway, then there would be a 10% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is different from 26.

Accepted Answer

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