Question

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.

2. 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.)

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

4. Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.01 significance level.

5. Estimate the p-value.

Answer 1

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.