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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 :

Answer:

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

Step-by-step explanation:

We are given the following information in the question:

n = 25

Sample mean, [tex]\bar{x}[/tex] = 29.530 inches

Alpha, α = 0.05

Sample standard deviation, s = 1.0953 inches

Confidence interval:

[tex]s^2 \pm t_{critical}\frac{s}{\sqrt{n}}[/tex]

Putting the values, we get,

[tex]t_{critical}\text{ at degree of freedom 24 and at}~\alpha_{0.05} = \pm 2.0638[/tex]

[tex](1.0953)^2 \pm 2.0638(\frac{1.0953}{\sqrt{25}} ) = 1.1996 \pm 0.452 = (0.7476,1.6516)[/tex]              

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