Question

The manufacturer claims that your new car gets 25 mpg on the highway. You suspect that the mpg is a different number for your car. The 57 trips on the highway that you took averaged 23.3 mpg and the standard deviation for these 57 trips was 4.3 mpg. What can be concluded at the αα = 0.10 level of significance?

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

H0:______________   

H1:_______________

3. The test statistic  t or 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: > or ≤ α
6. Based on this, we should: accept, fail to reject, or reject the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the sample mean is not significantly different from 25 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 23.3.
   • The data suggest that the populaton mean is significantly different from 25 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 25.
   • The data suggest that the population mean is not significantly different from 25 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 25.
8. Interpret the p-value in the context of the study.
   • There is a 0.42004138% chance of a Type I error.
   • If the population mean mpg for your car on the highway is 25 and if you take another 57 trips on the highway then there would be a 0.42004138% chance that the population mean would either be less than 23.3 or greater than 26.7.
   • If the population mean mpg for your car on the highway is 25 and if you take another 57 trips on the highway, then there would be a 0.42004138% chance that the sample mean for these 57 highway trips would either be less than 23.3 or greater than 26.7.
   • There is a 0.42004138% chance that the population mean mpg for your car on the highway is not equal to 25.
9. Interpret the level of significance in the context of the study.
   • If the population mean mpg for your car on the highway is 25 and if you take another 57 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 25.
   • There is a 10% chance that you own an electric powered car, so none of this matters to you anyway.
   • There is a 10% chance that the population mean mpg for your car on the highway is different from 25.
   • If the population population mean mpg for your car on the highway is different from 25 and if you take another 57 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 25.

Answer 1

a)
t-test

b)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 25
Alternative Hypothesis, Ha: μ ≠ 25

c)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (23.3 - 25)/(4.3/sqrt(57))
t = -2.985

d)
P-value Approach
P-value = 0.0042

e)
As P-value < 0.1,

f)
reject the null hypothesis.

g)
The data suggest that the populaton mean is significantly different from 25 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 25.

h)
option C

i)
option C