Question

In order to construct a confidence interval for the population variance, a random sample of n observations is drawn from a normal population. Use this information to find χ2α/2,df and χ21- α/2,df under the following scenarios. Use Table 3. (Round your answers to 3 decimal places.) χ²_α/2,df and χ²_{1- α/2,df} .

A 95% confidence level with n = 18.

b. A 95% confidence level with n = 30.

c. A 99% confidence level with n = 18.

d. A 99% confidence level with n = 30.

Answer 1

a 95% confidence level with n = 18.

df = n-1 = 18-1 = 17

?=1-C=1-0.95=0.05

?/2=0.05/2=0.025

1-?/2=1-0.025=0.975

We refer to the values of df=17 and 0.025 and 0.975 across the top row of chi square table.

?²_?/2,df= 30.191

?²_{1- ?/2,df} = 7.564

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b. A 95% confidence level with n = 30.

df = n-1 = 30-1 = 29

?=1-C=1-0.95=0.05

?/2=0.05/2=0.025

1-?/2=1-0.025=0.975

We refer to the values of df=29 and 0.025 and 0.975 across the top row of chi square table.

?²_?/2,df= 45.722

?²_{1- ?/2,df} = 16.047

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c. A 99% confidence level with n = 18.

df = n-1 = 18-1 = 17

?=1-C=1-0.99=0.01

?/2=0.01/2=0.005

1-?/2=1-0.005=0.995

We refer to the values of df=17 and 0.005 and 0.995 across the top row of chi square table.

?²_?/2,df= 35.718

?²_{1- ?/2,df} = 5.697

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d. A 99% confidence level with n = 30.

df = n-1 = 30-1 = 29

?=1-C=1-0.99=0.01

?/2=0.01/2=0.005

1-?/2=1-0.005=0.995

We refer to the values of df=29 and 0.005 and 0.995 across the top row of chi square table.

?²_?/2,df= 52.336

?²_{1- ?/2,df} = 13.121