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300     Chapter 8/Statistical intervals for a single sample


               8-86.     Consider the Izod impact test described in Exercise   length of the tolerance interval with the length of the 95% CI
               8-30. Compute a 99% tolerance interval on the impact strength   on the population mean. Which interval is shorter? Discuss the
               of PVC pipe that has conidence level 90%. Compare the length   difference in interpretation of these two intervals.
               of the tolerance interval with the length of the 99% CI on the   8-91.  Consider the television tube brightness data in Exercise
               population mean. Which interval is shorter? Discuss the differ-  8-37. Compute a 99% tolerance interval on the brightness of
               ence in interpretation of these two intervals.   the television tubes that has conidence level 95%. Compare the
               8-87.   Consider the syrup-volume data in Exercise 8-31.  length of the tolerance interval with the length of the 99% CI
               Compute a 95% tolerance interval on the syrup volume that  on the population mean. Which interval is shorter? Discuss the
               has conidence level 90%. Compare the length of the tolerance   difference in interpretation of these two intervals.
               interval with the length of the 95% CI on the population mean.  8-92.  Consider the strength-of-concrete data in Exercise 8-39.
               8-88.     Consider the margarine test described in Exercise 8-38.   Compute a 90% tolerance interval on the compressive strength
               Compute a 99% tolerance interval on the polyunsaturated fatty  of the concrete that has 90% conidence.
               acid in this particular type of margarine that has conidence level   8-93.  Consider the fuel rod enrichment data described in
               95%. Compare the length of the tolerance interval with the length   Exercise 8-43. Compute a 99% tolerance interval on rod
               of the 99% CI on the population mean. Which interval is shorter?   enrichment that has conidence level 95%. Compare the length
               Discuss the difference in interpretation of these two intervals.  of the tolerance interval with the length of the 95% CI on the
               8-89.  Consider the rainfall data in Exercise 8-35. Compute a   population mean.
               95% tolerance interval that has conidence level 95%. Compare   8-94.   Consider the bottle-wall thickness measurements
               the length of the tolerance interval with the length of the 95%   described in Exercise 8-42.
               CI on the population mean. Discuss the difference in interpreta-  (a)  Compute a 90% tolerance interval on bottle-wall thickness
               tion of these two intervals.                        that has conidence level 90%.
               8-90.     Consider the suspension rod diameter data in Exer-  (b) Compute a 90% lower tolerance bound on bottle-wall
               cise 8-40. Compute a 95% tolerance interval on the diameter   thickness that has conidence level 90%. Why would a
               of the rods described that has 90% conidence. Compare the  lower tolerance bound likely be of interest here?

               Supplemental Exercises



                  Problem available in WileyPLUS at instructor’s discretion.
                           Tutoring problem available in WileyPLUS at instructor’s discretion

               8-95.  Consider the conidence interval for μ  with known  sample variance is greater than or equal to 7.44? less than or
               standard deviation σ:                            equal to 2.56? For a random sample of size
                         x − z È  n ≤ μ ≤  x +  z α 2  σ  n     (a)  n = 16   (b)  n = 30    (c)  n = 71
                             α 1
               where  α  + α  = α. Let α  = 0.05 and ind the interval for  (d) Compare your answers to parts (a)–(c) for the approximate
                         2
               α  = α  1 = α/2 = 0.025. Now ind the interval for the case   probability that the sample variance is greater than or equal
                1   2                                              to 7.44. Explain why this tail probability is increasing or
               α  = 0.01 and α  = 0.04. Which interval is shorter? Is there any
                1         2                                        decreasing with increased sample size.
               advantage to a “symmetric” conidence interval?
                                                                (e)  Compare your answers to parts (a)–(c) for the approximate
               8-96.  A normal population has a known mean of 50 and
                                                                   probability that the sample variance is less than or equal
               unknown variance.
                                                                   to 2.56. Explain why this tail probability is increasing or
               (a)  A random sample of n = 16 is selected from this popula-  decreasing with increased sample size.
                  tion, and the sample results are x  = 52 and s  = 8. How  8-98.     An article in the Journal of Sports Science (1987,
                  unusual are these results? That is, what is the probability of   Vol. 5, pp. 261–271) presents the results of an investigation of
                  observing a sample average as large as 52 (or larger) if the   the hemoglobin level of Canadian Olympic ice hockey players.
                  known, underlying mean is actually 50?
                                                                The data reported are as follows (in g/dl):
               (b) A random sample of n = 30 is selected from this popula-
                  tion, and the sample results are x  = 52 and s  = 8. How  15.3  16.0  14.4  16.2     16.2
                  unusual are these results?                       14.9     15.7     15.3     14.6     15.7
               (c)  A random sample of n = 100 is selected from this popula-  16.0  15.0  15.7  16.2   14.7
                  tion, and the sample results are x  = 52 and s  = 8. How  14.8  14.6  15.6  14.5     15.2
                  unusual are these results?                    (a)  Given the following probability plot of the data, what is a logi-
               (d) Compare your answers to parts (a)–(c) and explain why  cal assumption about the underlying distribution of the data?
                  they are the same or different.               (b) Explain why this check of the distribution underlying the
               8-97.  A normal population has known mean μ  = 50 and  sample data is important if you want to construct a coni-
                       2
               variance σ  = 5. What is the approximate probability that the   dence interval on the mean.
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