Question

A simple random sample of

29

filtered​ 100-mm cigarettes is obtained from a normally distributed​ population, and the tar content of each cigarette is measured. The sample has a standard deviation of

0.20

mg. Use a

0.05

significance level to test the claim that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from

0.30

​mg, which is the standard deviation for unfiltered​ king-size cigarettes. Complete parts​ (a) through​ (d) below.

Answer 1

H0: = 0.30

Ha: 0.30

Test statistics

= ( n - 1) S2 / 2

= ( 29 - 1) * 0.202 / 0.302

= 12.44

Chi square critical values at 0.05 significance level with 28 df = 15.308 , 44.461

Since test statistics falls in rejection region, that is < 15.308, reject H0.

We conclude that we have sufficent evidence to support the claim that tar content of filtered​ 100-mm

cigarettes has a standard deviation different from 0.30mg