Question: A friend who hears that you are taking a statistics course asks for help with a specific

chemistry lab report. She has made four independent measurements of the specific

gravity of a compound. The results are: 4.72, 4.49, 4.64, 4.34. You are willing to

assume that the measurements are not biased. This means that the mean μ of the

distribution of measurements is the true specific gravity.

a. Calculate a 95% confidence interval for the true specific gravity for your friend.

b. Explain to your friend what this means.

c. What must be true about your friend’s measurements for your results in part (a) to be

correct?

d. You notice that the lab manual says that repeated measurements will vary according to

a normal distribution with standard deviation σ = 0.06. Redo the confidence interval

of part (a) using this additional information. Explain why we expect the new interval

to be shorter.

e. What critical value from the table would you use for an 80% confidence interval?

Without calculating that interval would you expect it to be wider or narrower than the

95% confidence interval?

f. The lab manual also asks whether the data show convincingly that the true specific

gravity is less than 4.5. State the null hypothesis used to answer this question. Then

calculate the test statistic and find its P-value. Use the lab manual’s value σ = 0.06and

calculate the P-value in detail.

g. Explain to your friend what your P-value means.