Question

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 H_a: σ² > 9 using α = 0.05.

State the test statistic. (Round your answer to two decimal places.)

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	<

Answer 1

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