Question

Use the given information to find the number of degrees of freedom, the critical values 2χ2L and χ2R, and the confidence interval estimate of sigma σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Platelet Counts of Women 98 % confidence; n=23 s=65.5.

df=22

(Type a whole number.)

2χ2L=9.542

(Round to three decimal places as needed.)

2χ2R=40.289

(Round to three decimal places as needed.)

The confidence interval estimate of σ is ___ < σ < ___

(Round to one decimal place as needed.)

Answer 1

Solution:

Given:

c = confidence level = 98%

n = sample size = 23

df = n - 1 = 23 - 1 = 22

s = sample standard deviation = 65.5

We have to construct 98% confidence interval estimate of sigma σ.

Formula:

where

and are chi-square critical values for c = 98% confidence level at 22 degrees of freedom.

Find

then

and

Thus

Thus

A 98% confidence interval estimate of σ is :