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: 3.82, 3.93, 3.67, and 3.78. You are willing to assume that the measurments are not biased. This means that the mean u 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 =0.15. 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 3.9. 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 standard deviation =0.15 and calculate the p-value in detail.

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

Here's my answers that are probably wrong.

A. 3.80 plus or minus 3.182(.054) =3.63 to 3.97

B. This means that 95% of the time the results of this experiment will be between 3.63 to 3.97

C. They must be between 3.63 to 3.97

D. 3.80 plus or minus 1.960(.15/sqrt 4)= 3.653 to 3.947 Because there is a smaller margin of error.

E. 1.282, Narrower

F. Ho: u=3.9 Ha: u < 3.9 3.80-3.9/(.15/sqrt 4)=-1.33 =.0918

G. It means that there is not good evidence that the true specific gravity is less than 3.9