The mean tar content of a simple random sample of 25 unfiltered king-size cigare

Question

The mean tar content of a simple random sample of 25 unfiltered king-size cigarettes is 21.1 mg, with a standard deviation of 3.2 mg. The mean tar content of a simple random sample of 25 filtered 100 mm cigarettes is 13.2 mg with a standard deviation of 3.7 mg.

Assume that the two samples are independent, simple, random samples, selected from normally distributed populations. Do not assume that the population standard deviations are equal.

o Use a 0.05 significance level to test the claim that unfiltered king-size cigarettes have mean tar content greater than that of filtered 100 mm cigarettes.

o What does the result suggest about the effectiveness of cigarette filters?

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 > mu2

where mu1 and mu2 are two population means.

The alternative hypothesis is right sided.

alpha = level of significance = 0.05

Here we use t-test for two samples because sample information is given.

This problem we can done by using TI-83 calculator.

X1bar = mean tar content of a unfiltered king-size cigarettes = 21.1 mg

s1 = standard deviation of a unfiltered king-size cigarettes = 3.2 mg

X2bar =  mean tar content of a filtered 100 mm cigarettes = 13.2 mg

s2 = standard deviation of a filtered 100 mm cigarettes = 3.7 mg

n1 = first sample size = 25

n2 = second sample size = 25

TI-83 steps :

STAT --> TESTS --> 4: 2-SampleTTest --> ENTER --> Highlight on Stats --> ENTER --> Input all the values --> select alternative ">"--> Pooled : No --> Calculate --> ENTER.

Output is,

t = 8.0747

P-value = 0.0000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Unfiltered king-size cigarettes have mean tar content greater than that of filtered 100 mm cigarettes.

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