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Answer:
95% confidence interval for the population variance of the number of tissues per box is [5043.11 , 23401.31].
Step-by-step explanation:
We are given that a consumer magazine counts the number of tissues per box in a random sample of 15 boxes of No- Rasp facial tissues. The sample standard deviation of the number of tissues per box is 97.
Firstly, the pivotal quantity for 95% confidence interval for the population variance is given by;
P.Q. = ~
where, = sample variance =
= 9409
n = sample of boxes = 15
= population variance
<em>Here for constructing 95% confidence interval we have used chi-square test statistics.</em>
So, 95% confidence interval for the population variance, is ;
P(5.629 < < 26.12) = 0.95 {As the critical value of chi-square at 14
degree of freedom are 5.629 & 26.12}
P(5.629 < < 26.12) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u><em>95% confidence interval for</em></u> = [
,
]
= [ ,
]
= [5043.11 , 23401.31]
Therefore, 95% confidence interval for the population variance of the number of tissues per box is [5043.11 , 23401.31].