A simple random sample of 28 filtered? 100-mm cigarettes is obtained from a norm

Question

A simple random sample of 28 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 0.18 mg. Use a 0.01 significance level to test the claim that the tar content of filtered? 100-mm cigarettes has a standard deviation different from 0.25 ?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?

b. Find the test statistic.

x^2=

c. Find the? P-value of the test statistic.

The? P-value of the test statistic is

d. State the conclusion.

(Reject/fail to reject) Ho. There (is/is not) sufficient evidence to conclude that the tar content of filtered? 100-mm cigarettes has a standard deviation different from 0.25 mg.

Explanation / Answer

The statistical software output for this problem is:

One sample variance summary hypothesis test:
?2 : Variance of population
H0 : ?2 = 0.0625
HA : ?2 ? 0.0625

Hypothesis test results:

Hence,

a) Hypotheses:

H0 : ? = 0.25
HA : ? ? 0.25

b) Test statistic = 13.9968

c) P - value = 0.0374

d) Fail to reject; is not

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