In: Statistics and Probability
A thermal interaction between two components requires that both components have similar temperature. One random sample for each component was obtained. The data is summarized in the table below:
Component 1 |
55 |
54 |
53 |
54 |
Component 2 |
54 |
52 |
53 |
a.
=54
=53
=0.8165
=1
b.
here we want to test H0 : the two components have the same temperature v/s H1: H0 is not true
i.e.H1: v/s H1:
the test statistic T=
where
= sample variance of the first sample
= sample variance of the second sample
= mean of the first sample
= mean of the second sample
=54
=53
=0.8165
=1
s2=pooled variance =0.8
T=1.46
we reject the null at level 0.05 if
= 2.571
here since
thus, we fail to reject the null hypothesis.thus, we can say that the components have the same temperature.
c.
the 95% CI is given by,
which is
(-0.756, 2.756)