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
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