[EX08-041] 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 6.15 (p. 330) are believed to have an extraction force that is normally distributed with a standard deviation of 36 Newtons.

a. A sample of 20 randomly chosen bottles is selected for testing.

Extraction Force in Newtons 296 338 341 261 250 347 336 297 279 297 259 334 281 284 279 266 300 305 310 253 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.

Extraction Force in Newtons 331.9 312.0 289.4 303.6 346.9 308.1 346.9 276.0 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 Newtons. Does either sample show sufficient reason to doubt the truthfulness of the claim? Explain.