Question

1. Solve this problem by hand.

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

1. Calculate x1,s1,x2,and s2
2. Is there evidence to support that the two components has the same temperature. Assume α=0.05 . Assume that both populations are normally distributed with equal unknown variances
3. Construct two sided 95% CI for part a

Answer 1

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)