Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. A simple random sample of 25 filtered 100 mm cigarettes is​ obtained, and the tar content of each cigarette is measured. The sample has a mean of 20.2 mg and a standard deviation of 3.81 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes.

What are the​ hypotheses?

A. H0​: μ>21.1 mg

H1​: μ<21.1 mg

B.H0​: μ=21.1 mg

H1​: μ<21.1 mg

C.H0​: μ<21.1 mg

   H1​: μ ≥ 21.1 mg

D. H0​: μ =21.1 mg

H1​: μ ≥ 21.1mg

Identify the test statistic.

t = _________

Identify the​ P-value.

The​ P-value is ___________

State the final conclusion that addresses the original claim. Choose the correct answer below.

A. Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

B. Reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

C. Reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

D.Fail to reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

What do the results​ suggest, if​ anything, about the effectiveness of the​ filters?

A.The results suggest that the filters are effective.

B.The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes.

C.The results do not suggest that the filters are effective.

D.The results suggest that the filters increase the tar content.

E.The results are inconclusive because the sample size is less than 30.

Answer 1

Solution :

= 21.1

=20.2

S= 3.81

n = 25

This is the left tailed test .

The null and alternative hypothesis is ,

B) H₀ :   = 21.1

H_a : < 21.1

Test statistic = t

= ( - ) / s  / n

= (20.2- 21.1) /3.81 / 25

= -1.18

P (Z < ) = 0.1246

P-value = 0.1246

= 0.05  

p= 0.1246 ≥ 0.05, it is concluded that the null hypothesis is not rejected.

A. Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

C.The results do not suggest that the filters are effective.