Answer:
(a) 900
(b) [567.35 , 1689.72]
(c) [23.82 , 41.11]
Step-by-step explanation:
We are given that a sample of 20 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 30 rooms i.e.;
Sample mean, = 290 Sample standard deviation, s = 30 and Sample size, n = 20
(a) Point estimate of the population variance is equal to sample variance, which is the square of Sample standard deviation ;
=
=
= 900
(b) 90% confidence interval estimate of the population variance is given by the pivotal quantity of ~
P(10.12 < < 30.14) = 0.90 {At 10% significance level chi square has critical
values of 10.12 and 30.14 at 19 degree of freedom}
P(10.12 < < 30.14) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
90% confidence interval for =
=
= [567.35 , 1689.72]
Therefore, 90% confidence interval estimate of the population variance is [567.35 , 1689.72] .
(c) 90% confidence interval estimate of the population standard deviation is given by ;
P( <
<
) = 0.90
90% confidence interval for =
= [23.82 , 41.11]
Therefore, 90% confidence interval estimate of the population standard deviation is [23.82 , 41.11] .