Question

The manufacturer claims that your new car gets 32 mpg on the highway. You suspect that the mpg is less for your car. The 64 trips on the highway that you took averaged 31.4 mpg and the standard deviation for these 64 trips was 8.9 mpg. What can be concluded at the αα = 0.01 level of significance?

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

H0:H0:  ? p μ  ? > < = ≠       

H1:H1:  ? p μ  ? > = < ≠    

3. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? > ≤  αα
6. Based on this, we should Select an answer accept reject fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the populaton mean is significantly less than 32 at αα = 0.01, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is less than 32.
   • The data suggest that the sample mean is not significantly less than 32 at αα = 0.01, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is less than 31.4.
   • The data suggest that the population mean is not significantly less than 32 at αα = 0.01, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is less than 32.
8. Interpret the p-value in the context of the study.
   • If the population mean mpg for your car on the highway is 32 and if you take another 64 highway trips, then there would be a 29.57815389% chance that the population mean mpg for your car on the highway would be less than 32.
   • If the population mean mpg for your car on the highway is 32 and if you drive another 64 times, then there would be a 29.57815389% chance that the sample mean for these 64 trips would be less than 31.4.
   • There is a 29.57815389% chance of a Type I error.
   • There is a 29.57815389% chance that the population mean mpg for your car on the highway is less than 32.
9. Interpret the level of significance in the context of the study.
   • If the population population mean mpg for your car on the highway is less than 32 and if you take another 64 trips on the highway, then there would be a 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is equal to 32.
   • There is a 1% 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 32 and if you take another 64 trips on the highway, then there would be a 1% chance that we would end up falsely concluding that the population mean mpg for your car on the highway is less than 32.
   • There is a 1% chance that the population mean mpg for your car on the highway is less than 32.

Answer 1