Question

A simple random sample from a population with a normal distribution of 100 body temperatures has

x overbar =9 8.40°F ands = 0.62°F.

Construct a 98​% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Is it safe to conclude that the population standard deviation is less than 2.10°F​?

___°F < σ < ___°F

​(Round to two decimal places as​ needed.)

Is it safe to conclude that the population standard deviation is less than 2.10°F​?

A.This conclusion is not safe because 2.10°F is in the confidence interval.

B.This conclusion is safe because 2.10°F is in the confidence interval.

C.This conclusion safe because 2.10°F is outside the confidence interval.

D.This conclusion is not safe because 2.10°F is outside the confidence interval.

Answer 1

Chi square critical values at 0.02 level with 99 df = 69.23 , 134.642

98% Confidence interval is

Sqrt [ ( n -1 ) S² / /2 ] < < Sqrt [ ( n -1 ) S² / 1-/2 ]

Sqrt [ 99 * 0.62² / 134.642 ] < < Sqrt [ 99 * 0.62² / 69.23 ]

0.53 < < 0.74

This conclusion safe because 2.10°F is outside the confidence interval.