SOLUTION: A car dealer states that a new brand of car gets 35 miles per gallon on average. Suppose a consumer group claims that these cars get less than 35 miles per gallon. A sample of 40

Question 1120540: A car dealer states that a new brand of car gets 35 miles per gallon on average. Suppose a consumer group claims that these cars get less than 35 miles per gallon. A sample of 40 cars is selected, and the sample mean for the 40 cars is 33 miles per gallon while the standard deviation is 3.8.
1) State the null and alternative hypotheses for this test.
2) Calculate the test statistic for this test. Explain what this test statistic represents.
3) Use technology to calculate the p-value for this test. Explain what this p-value represents.
4) State the conclusion for this test at the 0.05 level of significance. Do you think the car dealer is telling the truth? Why or why not?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Ho: mean is >=35
Ha: mean is not
alpha=0.05
test stat is a t 0.95, df=39
critical value t < -1.69. If the test statistic is less than -1.69, it will be considered to be outside the possibility of a chance random effect. One way test
test statistic t=(33-35)/3.8/sqrt (40) (mbar-mean)/s/sqrt(n)
t=-2*sqrt(40)/3.8=-3.33. This is the number of sd s in the t-distribution for data with a mean of 35 and s of 3.8 with df=39.
p value=0.001. If the null hypothesis were true, the probability of getting a result of this magnitude or less is one in a thousand.
Reject Ho and conclude that the mean is less than 35 mpg.
There are many such reasons for this including the dealer is not telling the truth; that is not a statistical conclusion given what is given.

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