Answers to a One Sample t Test
The following will assist you in understanding more the hypothesis process, and prepare you for the Applications
1 activity in Week Two.
"The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow the normal
distribution. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a
mean life of 311 days with a sample standard deviation of 12 days. Did the modification
increase
the mean life
of the battery? ‘
The level of significance for this problem is 0.05.
Setup the null hypothesis and alternative hypothesis.
Ho:
μ
≤
305
H
1
:
μ
> 305
Note that in a hypothesis set up we are looking for one of three possibilities that the "situation" is asking: is there
a
difference
in the mean, is there an
increase
from the mean, or is there a
decrease
from the mean? I have
put the key words in bold. In the "last sentence" above, note the key word is
increase.
Important: when there is
a direction (increase/more than or a decrease/less than) that direction is always in the alternative. If there is no
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 Spring '10
 Regis
 Statistics, Normal Distribution, Null hypothesis, Statistical hypothesis testing, critical value, Hypothesis Set Ups

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