Question

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The following data represents the age (in weeks) at which babies first crawl based on a survey of 12 mothers. The data is approximately normal with a sample standard deviation of 10.00 weeks. Construct and interpret a 95% confidence interval for the population standard deviation of the age at which babies first crawl [52 30 44 35 39 26 47 37 56 26 39 28]

Answer 1

Solution :

Given that,

s = 10

s² = 100

n = 12

Degrees of freedom = df = n - 1 = 11

At 95% confidence level the ² value is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

1 - / 2 = 1 - 0.025 = 0.975

²_L = ²_/2,df = 21.92

²_R = ²_{1 - /2,df} = 3.816

The 95% confidence interval for is,

(n - 1)s² / ²_/2 < < (n - 1)s² / ²_{1 - /2}

  12 * 100 / 21.92 < < 12 * 100 / 3.816

7.08 < < 16.98

(7.08 , 16.98 )