Question

# Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time...

Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (−) in seconds per week.

 −0.25 −0.28 −0.14 −0.26 +0.27 −0.20 +0.32 +0.31 −0.14 −0.32 −0.65 −0.45 −0.50 −0.69 −0.04 −0.16 −0.53 +0.08

1. State the null hypothesis and the alternate hypothesis.
1. State the decision rule for 0.01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
1. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
1. Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.01 significance level.
1. Estimate the p-value.

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 0
Alternative Hypothesis, Ha: μ ≠ 0

Decision Rule
This is two tailed test, for α = 0.01 and df = 17
Critical value of t are -2.898 and 2.898.
Hence reject H0 if t < -2.898 or t > 2.898

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (-0.2 - 0)/(0.3063/sqrt(18))
t = -2.77

No, it is not reasonable to conclude that the mean gain or loss in time for the watches is 0

P-value Approach
P-value = 0.0131
As P-value >= 0.01, fail to reject null hypothesis.

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