Does the computer overestimate mpg, if the vehicle is known to average 40 mpg?

[PharmlyDoc]

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This is a statistics problem....I'm given a sample size of 20 (calculations that a car computer computes for mpg). And sample mean xbar is 43.17. And the standard deviation is known to be 3.5 mpg.

I was asked to compute a 95% confidence interval and I got 41.6 to 44.7.

Now I'm asked... It is suspected that the computer overestimates the miles per gallon. If this vehicle is known to average 40 mpg, is there convincing evidence that the computer overestimates the miles per gallon? Explain why or why not (Hint: Compute a p-value and use the result of the 95% confidence interval.

I use a z test, where i measure the difference between the test statistic and the unknown parameter. I keep getting a z-score of 4.1 and a p value of 2.6*E^-5

 

[FeinMS]

You'll find the answer to this question tens of years later when MCAT incorporates statistics as one of the subject.
Looks like you can say with 95% confidence that the computers overestimate the mpg because 40 is not in your 95% confidence interval (assuming you found your interval correctly.) z score of 4.1 doesn't make sense because 40 is definitely less than 43.17. You should expect a negative z score.

 

[PharmlyDoc]

Well this question doesn't make any since to me. You pre-meds are smart, help a pre-pharm out!

When the question says that it is known to average 40 mpg then that is our null hypothesis. mu=40. So the alternative hypothesis would be mu>40.

I plug this information into my ti-84 and I keep getting z score 4.1 and p-value 2.6*E^-5.

the z score is supposed to be the difference between the mean of the test statistic, which in this case is 43.17, and the true parameter, which is the true mean mpg. So my interpretation is that it is claimed that the car gets 40 mpg,