Question

The manufacturer claims that your new car gets 31 mpg on the highway. You suspect that the mpg is a different number for your car. The 40 trips on the highway that you took averaged 28.7 mpg and the standard deviation for these 40 trips was 5.8 mpg. What can be concluded at the α α = 0.01 level of significance? a.For this study, we should use Select an answer z-test for a population proportion t-test for a population mean b.The null and alternative hypotheses would be: H0: H0: ? μ p ? ≠ = > < H1: H1: ? μ p ? > < = ≠ c.The test statistic ? t z = (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 ? ≤ > α α f.Based on this, we should Select an answer reject fail to reject accept the null hypothesis. g.Thus, the final conclusion is that ... The data suggest that the sample mean is not significantly different from 31 at α α = 0.01, so there is statistically insignificant evidence to conclude that the sample mean mpg for your car on the highway is different from 28.7. The data suggest that the population mean is not significantly different from 31 at α α = 0.01, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is different from 31. The data suggest that the populaton mean is significantly different from 31 at α α = 0.01, so there is statistically significant evidence to conclude that the population mean mpg for your car on the highway is different from 31. h.Interpret the p-value in the context of the study. There is a 1.64116434% chance of a Type I error. If the population mean mpg for your car on the highway is 31 and if you take another 40 trips on the highway then there would be a 1.64116434% chance that the population mean would either be less than 28.7 or greater than 33.3. There is a 1.64116434% chance that the population mean mpg for your car on the highway is not equal to 31. If the population mean mpg for your car on the highway is 31 and if you take another 40 trips on the highway, then there would be a 1.64116434% chance that the sample mean for these 40 highway trips would either be less than 28.7 or greater than 33.3. i.Interpret the level of significance in the context of the study. There is a 1% chance that you own an electric powered car, so none of this matters to you anyway. If the population population mean mpg for your car on the highway is different from 31 and if you take another 40 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 31. There is a 1% chance that the population mean mpg for your car on the highway is different from 31. If the population mean mpg for your car on the highway is 31 and if you take another 40 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 different from 31.

Answer 1

e) The p-value is > α

f) Based on this, we should fail to reject accept the null hypothesis

g) Thus, the final conclusion is that -

The data suggest that the population mean is not significantly different from 31 at α α = 0.01, so there is statistically insignificant evidence to conclude that the population mean mpg for your car on the highway is different from 31.

h) If the population mean mpg for your car on the highway is 31 and if you take another 40 trips on the highway, then there would be a 1.64116434% chance that the sample mean for these 40 highway trips would either be less than 28.7 or greater than 33.3

i)  If the population mean mpg for your car on the highway is 31 and if you take another 40 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 different from 31.