Watch Corporation of Switzerland claims that its watches on average will neither

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. –0.38 –0.20 –0.38 –0.32 +0.32 –0.23 +0.30 +0.25 –0.10 –0.37 –0.61 –0.48 –0.47 –0.64 –0.04 –0.20 –0.68 +0.05

Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the .05 significance level. At a level of .05 significance, we reject H0: = 0 if t < _____ or t > _____. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Explanation / Answer

Here H0 : = 0

Ha : 0

Here n = 18 so dF = 18 -1 = 17 and alpha = 0.05

tcritical = t17,0.05 = 2.1098

so we will reject the null if t < -2.1098 or t > 2.1098

so here sample mean x = -0.2322

sample standard deviation s = 0.312

here test statistic

t = x/ s/ sqrt(n) = -0.2322/ (0.312/ sqrt(18)) = -0.2322/ 0.0735 = -3.159

so here t < tcritical

so we shall reject the null hypothesis and reject the claim that Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week.

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