# Question: The force required to extract a cork from a wine

The force required to extract a cork from a wine bottle is an important property of the cork. If the force is too little, the cork probably is not a good protector of the wine inside. If the force is too great, it will be difficult to remove. Neither is desirable. The no. 9 corks in Applied Example 6.13 (p. 285) are believed to have an extraction force that is normally distributed with a standard deviation of 36 New tons.
a. A sample of 20 randomly chosen bottles is selected for testing.
Find the 98% confidence interval for the mean extraction force.
b. During a different testing, a sample of eight bottles was randomly selected and tested.
Find the 98% confidence interval for the mean extraction force.
c. What effect did the two different sample means have on the answers in parts a and b? Explain.
d. What effect did the two different sample sizes have on the answers in parts a and b? Explain.
e. The mean extraction force was claimed to be 310 New tons. Does either sample show sufficient reason to doubt the truthfulness of the claim? Explain.

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