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 0.22 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 0.35 mg, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below.
A simple random sample of 26 filtered 100-mm cigarettes is obtained from a
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Part 1
a. What are the null and alternative hypotheses?
A.
H0: σ=0.35 mg
H1: σ<0.35 mg
B.
H0: σ=0.35 mg
H1: σ≠0.35 mg
C.
H0: σ≠0.35 mg
H1: σ=0.35 mg
D.
H0: σ>0.35 mg
H1: σ≤0.35 mg
Part 2
b. Find the test statistic.
χ2=enter your response here (Round to three decimal places as needed.)
Part 3
c. Find the P-value of the test statistic.
The P-value of the test statistic is enter your response here.
(Round to three decimal places as needed.)
Part 4
d. State the conclusion.
▼
Fail to reject
Reject
H0. There
▼
is
is not
sufficient evidence to conclude that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.35 mg.
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