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. Picture Click here for the Excel Data File –0.21 –0.19 –0.15 –0.16 +0.25 –0.24 +0.32 +0.43 –0.15 –0.39 –0.41 –0.55 –0.52 –0.67 –0.05 –0.28 –0.26 +0.03

Chapter 10 Quiz K o Question 18 (of 18) 18 value: 10.00 points Watch Corporation of Switzerland claims that its watches on average w neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+)or losses in seconds per week. Click here for the Excel Data File -0.21 -0.19 -0.15 -0.16 0.25 -0.24 +0.32 +0.43 -0.15 39 -0.41 -0.55 -0.52 -0.67 -0.05 -0.28 -0.26 +0.03 a-1. 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 Ho: u o if t

Explanation / Answer

Given that,
population mean(u)=0
sample mean, x =0.33334
standard deviation, s =0.168795
number (n)=18
null, Ho: <0
alternate, H1: >0
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.74
since our test is right-tailed
reject Ho, if to > 1.74
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =0.33334-0/(0.168795/sqrt(18))
to =8.378
| to | =8.378
critical value
the value of |t | with n-1 = 17 d.f is 1.74
we got |to| =8.378 & | t | =1.74
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 8.3785 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: <0
alternate, H1: >0
test statistic: 8.378
critical value: 1.74
decision: reject Ho
p-value: 0

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