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

ID: 2921366 • Letter: W

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.

–0.45

–0.19

–0.16

–0.20

+0.28

–0.24

+0.46

+0.26

–0.14

–0.37

–0.32

–0.50

–0.51

–0.62

–0.04

–0.19

–0.56

+0.04

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.)

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.

Explanation / Answer

Given that,
population mean(u)=0
sample mean, x =-0.1917
standard deviation, s =0.3034
number (n)=18
null,the mean gain or loss in time for the watches is 0 Ho: =0
alternate, the mean gain or loss in time for the watches is not zero, H1: !=0
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.11
since our test is two-tailed
reject Ho, if to < -2.11 OR if to > 2.11
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =-0.1917-0/(0.3034/sqrt(18))
to =-2.681
| to | =2.681
critical value
the value of |t | with n-1 = 17 d.f is 2.11
we got |to| =2.681 & | t | =2.11
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -2.6807 ) = 0.0158
hence value of p0.05 > 0.0158,here we reject Ho
ANSWERS
---------------
null, Ho: =0
alternate, H1: !=0
test statistic: -2.681
critical value: -2.11 , 2.11
decision: reject Ho
p-value: 0.0158, between 0.010 and 0.02