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. Picture Click here for the Excel Data File −0.16 −0.15 −0.20 −0.17 +0.26 −0.19 +0.30 +0.43 −0.10 −0.31 −0.48 −0.44 −0.51 −0.67 −0.05 −0.24 −0.51 +0.05

A. State the null hypothesis and the alternate hypothesis.

H0= (mean symbol) =

H1= (mean symbol) =

B. 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.)

  At a level of 0.05 significance, we reject H0: (mean symbol) = 0 if t < _____________ or t > ____________.

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

Value of the test statistic:

D. It reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.05 significance level.

_______(reject/do not reject) H0. It ____ (is/is not) reasonable to conclude that the mean gain or loss in time for the watches is 0.

E. Estimate the p-value.

The p-value is: _______

Answer 1

necessary calculation table:-

data (x)	x2
-0.16	0.0256
-0.15	0.0225
-0.2	0.04
-0.17	0.0289
0.26	0.0676
-0.19	0.0361
0.3	0.09
0.43	0.1849
-0.1	0.01
-0.31	0.0961
-0.48	0.2304
-0.44	0.1936
-0.51	0.2601
-0.67	0.4489
-0.05	0.0025
-0.24	0.0576
-0.51	0.2601
0.05	0.0025
sum=-3.14	sum=2.0574

sample size (n) = 18

a).hypothesis:-

B). At a level of 0.05 significance, we reject H₀:-

[ df = (n-1 )= (18-1) = 17

using t distribution table, t critical value for df= 17,alpha=0.05, both tailed test = 2.110 ]

C).the test statistic is:-

D. here, we have,

We reject H₀. It is not reasonable to conclude that the mean gain or loss in time for the watches is 0.

E. The p-value is:-

between 0.02 and 0.05

[ using t distribution table for df = 17 , t score = -2.483,both tailed test.]

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