[EX09-061] Length is not very important in evaluating the quality of corks because it has little to do with the effectiveness of a cork in preserving wine. Winemakers have several lengths to choose from and order the length cork they prefer (long corks tend to make a louder pop when the bottle is uncorked). Length is monitored very closely, though, because it is a specified quality of the cork.

The lengths of no. 9 natural corks (24 mm diameter by 45 mm length) have a normal distribution.

Twelve randomly selected corks were measured to the nearest hundredth of a millimeter.

44.95 44.95 44.80 44.93 45.22 44.82 45.12 44.62 45.17 44.60 44.60 44.75

a. Does the preceding sample give sufficient reason to show that the mean length is different than 45.0 mm, at the 0.02 level of significance?

A different random sample of 18 corks is taken from the same batch.

45.17 45.02 45.30 45.14 45.35 45.50 45.26 44.88 44.71 44.07 45.10 45.01 44.83 45.13 44.69 44.89 45.15 45.13

b. Does the preceding sample give sufficient reason to show that the mean length is different than 45.0 mm, at the 0.02 level of significance?

c. What effect did the two different sample means have on the calculated test statistic in parts a and b? Explain.

d. What effect did the two different sample sizes have on the calculated test statistic in parts a and b? Explain.

e. What effect did the two different sample standard deviations have on the calculated test statistic in parts a and b? Explain.