A manufacturer of watches has established that on the average his watches do not gain or lose. He also would like to claim that at least 95% of the watches are accurate to ±0.2 s per week. A random sample of 15 watches provided the following gains (+) or losses (−) in seconds in one week:

+0.17 −0.07 +0.13 −0.05 +0.23

+0.01 +0.06 +0.08 −0.14 −0.10

+0.08 +0.11 +0.05 −0.87 +0.05 Can the claim be made with a 5% chance of being wrong? (Assume that the inaccuracies of these watches are normally distributed.)

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