Question

n 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 χ²_α/2,df and χ²_1-α/2,df under the following scenarios. (Round your answers to 3 decimal places. You may find it useful to reference the appropriate table: chi-square table or F table)

		χ2α/2,df	χ21-α/2,df
a.	A 90% confidence level with n = 11.
b.	A 90% confidence level with n = 42.
c.	A 95% confidence level with n = 11.
d.	A 95% confidence level with n = 42.

Answer 1

1. Given : d.f.=degrees of freedom=n-1=11-1=10

Significance level=

; The Excel function is , =CHIINV(0.05,10)

  ; The Excel function is , =CHIINV(0.95,10)

2. Given : d.f.=degrees of freedom=n-1=42-1=41

Significance level=

; The Excel function is , =CHIINV(0.05,41)

  ; The Excel function is , =CHIINV(0.95,41)

3. Given : d.f.=degrees of freedom=n-1=11-1=10

Significance level=

; The Excel function is , =CHIINV(0.025,10)

  ; The Excel function is , =CHIINV(0.975,10)

4. Given : d.f.=degrees of freedom=n-1=42-1=41

Significance level=

; The Excel function is , =CHIINV(0.025,41)

; The Excel function is , =CHIINV(0.975,41)