Question

The age in weeks at which babies first crawl is assumed to be normally distributed. A survey of 15 mothers conducted by Essential Baby resulted in a sample standard deviation of s = 12 . A) In order to construct a 90% confidence interval, we must determine the values α/2 and (1 − α/2) . Determine the two values. B) Construct a 90% confidence interval for the population standard deviation of the age (in weeks) at which babies first crawl.

Answer 1

Solution :

Given that,

c = 0.90

s = 12

n = 15

A)

At 90% confidence level the is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

/2,df = 0.05,14 = 23.68

and

1- /2,df = 0.95,14 = 6.57

2L = 2/2,df = 23.68

2R = 21 - /2,df = 6.57

B)

The 90% confidence interval for is,

s (n-1) / /2,df < < s (n-1) / 1- /2,df

12 ( 15 - 1 ) / 23.68 < < 12 ( 15 - 1 ) / 6.57

9.23 < < 17.52

( 9.23 , 17.52 )