A watch manufacturer claims that their watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gain (+) or losses (-) in seconds per week....

A watch manufacturer claims that their watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gain (+) or losses (-) in seconds per week.

-0.61 -0.37 -0.38 -0.32 +0.32 -0.23 -0.20 -0.68 -0.10

-0.20 -0.38 -0.48 -0.47 -0.64 -0.04 +0.30 +0.25 +0.05

(a)  What is the point estimate for the true average gain or losses in seconds per week of the watches produced by the manufacturer?

(b)  Find the 98% confidence interval for the mean gain or loss in time for the watches.

(c)  Test, at the 0.02 level of significance, whether the mean gain or loss in time for the watches is 0. Is the manufacturer’s claim correct?

(d)  Compute the p-value for the test in (c).

(e)  State the assumption for the test in (c).

(f)  Are the results of (b) and (c) consistent?