Answer:
95% confidence interval for the population variance = (1.42 , 2.62).
Step-by-step explanation:
We are given that the weights of 83 randomly selected windshields were found to have a variance of 1.88.
<em>So, firstly the pivotal quantity for 95% confidence interval for the population variance is given by;</em>
P.Q. = ~
where, = sample variance = 1.88
= population variance
n = sample of windshields = 83
So, 95% confidence interval for population variance, is;
P(58.85 < < 108.9) = 0.95 {As the table of
at 82 degree of freedom
gives critical values of 58.85 & 108.9}
P(58.85 < < 108.9) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<em><u>95% confidence interval for</u></em> = (
,
)
= ( ,
)
= (1.42 , 2.62)
Therefore, 95% confidence interval for the population variance of the weights of all windshields in this factory is (1.42 , 2.62).