Question

# Use the data to calculate the sample variance, s2. (Round your answer to five decimal places.)...

Use the data to calculate the sample variance, s2. (Round your answer to five decimal places.)

n = 10:

19.1, 9.5, 11.8, 8.8, 10.8, 8.8, 7.0, 12.6, 14.8, 12.4

s2 =

Construct a 95% confidence interval for the population variance, σ2. (Round your answers to two decimal places.)

?  to ?

Test H0: σ2 = 9 versus Ha: σ2 > 9 using α = 0.05.

χ2 =

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to four decimal places.)

 χ2 > χ2 <

variance, s2 = 12.22711

α = 1 - 0.95 = 0.05
The critical values for α = 0.05 and df = 9 are Χ^2(1-α/2,n-1) = 2.7 and Χ^2(α/2,n-1) = 19.023

CI = (9*3.4967^2/19.023 , 9*3.4967^2/2.7)
CI = (5.78 , 40.76)

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (10 - 1)*12.22711/9
Χ^2 = 12.23

Rejection Region
This is right tailed test, for α = 0.05 and df = 9
Critical value of Χ^2 is 16.919
Hence reject H0 if Χ^2 > 16.919

χ2   > 16.919
χ2   < NONE