Question

Skagen-Tvosky Clock Manufacturers, LLC claim that their wall clocks on average will neither gain nor lose time throughout the week. A sample of 18 wall clocks showed the following gains (+) or losses (-) in seconds per week. Is it reasonable to conclude that the mean gain or loss in time for the watches is 0?

0.10	0.10	0.40	-0.32	-0.30	-0.23	-0.20	0.25	-0.10
-0.37	-0.61	0.20	-0.30	-0.64	0.40	-0.20	-0.68	-0.40

A.)	State the decision rule for 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Reject H0: μ = 0 if t < ____________

or t > ________

B.)	Compute the Value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Value of the test statistic:

_____________

Answer 1

Using Excel we get, sample size (n) = 18

sample mean = -0.1611

sample standard deviation = 0.3380

The null and alternative hypotheses are,

H0 : μ = 0

Ha : μ ≠ 0

A) t-critical values at significance level of 0.05 with degrees of freedom = 18 - 1 = 17 are, t^* = 2.110

Excel Command : =TINV(0.05, 17) = 2.110

Decision Rule : Reject H0 : μ = 0 if, t < -2.110 or t > 2.110

B) Test statistic is,

=> The value of the test statistic = -2.02

Since, test statistic = -2.02 > -2.110, we fail to reject H0.

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