A simple random sample of 26 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.a. What are the null and alternative hypotheses?A.H0: sigmagreater than0.30 mgUpper H 1 : sigma less than or equals 0.30 mgB.H0: sigmaequals0.30 mgUpper H 1 : sigma not equals 0.30 mgYour answer is correct.C.H0: sigmanot equals0.30 mgUpper H 1 : sigma equals 0.30 mgD.H0: sigmaequals0.30 mgUpper H 1 : sigma less than 0.30 mgb. Find the test statistic.

There is significant evidence to conclude that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg, which is the standard deviation for unfilteredking-size cigarettes

Step-by-step explanation:

sample size, n = 26

sample std. dev., s = 0.20

H0: sigma = 0.30

Ha: sigma not equals to 0.30

Test statistic,

chi-square = (n-1)*s^2/sigma^2

chi-square = 25 * 0.20^2/0.30^2

= 25*0.04*0.09

=0.09

Critical values are 15.31, 44.46

As the test statistic is less than the critical value 15.31, hence reject the null hypothesis.

There is significant evidence to conclude that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg, which is the standard deviation for unfilteredking-size cigarettes