In: Statistics and Probability
You randomly select and weigh 23samples of an allergy medication. The sample standard deviation is 1.56milligrams. Assuming the weights are normally distributed, construct 95% confidence intervals for the population variance and standard deviation.Please interpret your result.
Solution :
Given that,
n = 23
df = 22
2R
=
2
/2,df
= 36.781
2L
=
21 -
/2,df = 10.982
The 95% confidence interval for
2 is,
(n - 1)s2 /
2
/2
<
2 < (n - 1)s2 /
21 -
/2
22 * 1.562 / 36.781 <
2 < 22 * 1.562 / 10.982
1.2065 <
2 < 2.2079
(1.2065 , 2.2079 , )