I don't want to copy it verbatim in case the prof is watching. We are given the sample data of non-normal population. The prof is asking us to determine whether it's likely that the population mean is 38. Also, he has stated that we should choose either the Z-test, t-test, or f-test. He also said it's not likely the Z because z is only for normal distributions.

I immediately worked out the descriptive statistics:

Xbar = 38.39

Sample standard deviation = 0.42

Count = 31

And starting working out the critical values for the T-Test, but I realized that I can't do this because if the population is non-normal, therefore the sample should also be non-normal, correct?

We learned about the central limit theorem in class, but i'm not sure how it would apply here. Perhaps I could use the mean of this sample to create a distribution of means? However this doesn't help me because the count would only be 1, and therefore the degrees of freedom would be 0. I couldn't use the Z-test here either because I don't know the population standard deviation.

I hope someone can help me. The raw data is below.

Thanks!

32

35

35

36

36

36

37

37

37

37

38

38

38

38

38

39

39

39

39

39

39

39

40

40

40

40

41

41

41

43

43