A winemaker has placed a large order for the no. 9 corks described in Applied Example 6.13 (p. 285) and is concerned about the number of corks that might have smaller diameters. During the corking process, the corks are squeezed down to 16 to 17 mm in diameter for insertion into bottles with an 18 mm opening. The cork then expands to make the seal. The winemaker wants the corks to be as tight as possible and is therefore concerned about any that might be undersize
d. The diameter of each cork is measured in several places, and an average diameter is reported for each cork. The cork manufacturer has assured the winemaker that each cork has an average diameter within the specs and that all average diameters have a normal distribution with a mean of 24.0 mm.
a. Why does it make sense for the diameter of the cork to be assigned the average of several different diameter measurements? A random sample of 18 corks is taken from the batch to be shipped and the diameters (in millimeters) obtained:
b. The average diameter spec is 24 mm + 0.6 mm/ - 0.4 mm Does it appear this order meets the spec on an individual cork basis? Explain.
c. Does the sample in part a show sufficient reason to doubt the truthfulness of the claim, that the mean average diameter is 24.0 mm, at the 0.02 level of significance? A different sample of 18 corks was randomly selected and the diameters (in millimeters) obtained:
d. Does the preceding sample show sufficient reason to doubt the truthfulness of the claim, that the mean average diameter is 24.0 mm, at the 0.02 level of significance?
e. What effect did the two different sample means have on the calculated test statistic in parts c and d? Explain.
f. What effect did the two different sample standard deviations have on the calculated test statistic in parts c and d? Explain.