She has made four independent measurements of the specific gravity of a compound ...

     Z and T Statistics: Confidence Intervals and   Significance Tests: 7 points                    chemistry   lab report. She has made four independent measurements of the specific        gravity   of a compound. The results are: 4.65, 4.7, 4.42 and 4.26. 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 s = 0.18. 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 s =   0.18and       calculate   the P-value in detail.        g.   Explain to your friend what your P-value means.