Question

The following data represent the age​ (in weeks) at which babies first crawl based on a survey of 12 mothers. The data are normally distributed and sequals9.190 weeks. Construct and interpret a 95​% confidence interval for the population standard deviation of the age​ (in weeks) at which babies first crawl. 49 31 43 35 37 26 46 36 55 26 38 29

A. If repeated samples are​ taken, 95​% of them will have the sample standard deviation between ___ and ___

B.There is 95% confidence that the population standard deviation is between __ and __

C.There is a 95% probability that the true population standard deviation is between __ and __

Answer 1

Solution:

Given:

Sample size = n = 12

Sample standard deviation = s = 9.190

Confidence level = c = 95%

Construct and interpret a 95​% confidence interval for the population standard deviation of the age​ (in weeks) at which babies first crawl.

Formula:

where

and are chi-square critical values for right and left tails.

c = 0.95 , then

Area for right tail critical value:

and Area for left tail critical value:   

df = n - 1 = 12 - 1 = 11

Thus we get:

   and

Thus we get:

_{(Round final answer to specified number of decimal places)}

Interpretation:

B.There is 95% confidence that the population standard deviation is between 6.51 and 15.60.

_{(Round final answer to specified number of decimal places)}