Question

Scores on an IQ test are normally distributed. A sample of 12 IQ scores had standard deviation s=6 (a) Construct a 95% confidence interval for the population standard deviation σ. Round the answers to at least two decimal places. (b) The developer of the test claims that the population standard deviation is σ=7 Does this confidence interval contradict this claim? Explain.

Answer #1

**Answer**:

a)

Given,

degree of freedom = n - 1

= 12 - 1

= 11

alpha = 0.05

alpha/2 = 0.025

(0.025,11) = 21.92004926 [since from critical chi square table]

(0.975,11) = 3.81574825

To construct 95% CI

Interval = (sqrt((n-1)s^2/(alpha/2) , sqrt((n-1)s^2/(1-alpha/2))

= sqrt(11*6^2/21.92) , sqrt(11*6^2/3.82)

= (18.07 , 10.18)

b)

Ho : σ = 7

Ha : σ != 7

Here we can say yes, due to that the CI doesn't contain 7

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