Question

A pediatrician's records showed the mean height of a random sample of 25 girls at age 12 months to be 29.530 inches with a standard deviation of 1.0953 inches. Construct a 95% confidence interval for the population variance. (Round your answers to 4 decimal places.)

Answer 1

Confidence interval for the population variance = (0.7476,1.6516)

Explanation:

We are given the following information in the question:

n = 25

Sample mean,
`\bar{x}` = 29.530 inches

Alpha, α = 0.05

Sample standard deviation, s = 1.0953 inches

Confidence interval:

`s^2 \pm t_(critical)(s)/(√(n))`

Putting the values, we get,

`t_(critical)\text{ at degree of freedom 24 and at}~\alpha_(0.05) = \pm 2.0638`

`(1.0953)^2 \pm 2.0638((1.0953)/(√(25)) ) = 1.1996 \pm 0.452 = (0.7476,1.6516)`