Question

1. The Carolina Tobacco Company advertised that its best-selling nonfiltered cigarettes contain at most 40 mg of nicotine, but Consumer Advocate magazine ran tests of 10 randomly selected cigarettes and found the amounts (in mg) shown in the list below. It’s a serious matter to charge that the company advertising is wrong, so the magazine editor chooses a significance level of α = 0.01 in testing her belief that the mean nicotine content is greater than 40 mg. Using a 0.01 significance level, test the editor’s belief that the mean is greater than 40 mg. 47.3 39.3 40.3 38.3 46.3 43.3 42.3 49.3 40.3 46.3 Show all the steps of your hypothesis test including a) the claim being tested , b) the null and alternative hypothesis, c) the test statistic, d) the p value, e) initial conclusion, and f) a final conclusion about the original claim.

Answer 1

Consider X :Amount of nicotine in non filtered cigarettes.

Let : Mean amount of nicotine in non filtered cigarettes.

We have to test the hypothesis that

Whether or mean amount of nicotine in non filtered cigarettes is greater than 40 mg or not?

i.e. Null Hypothesis - against

Alternative Hypothesis - ( Right-tailed test)

Since population variance is unknown, we used one sample t-test for testing population mean.

The value of test statistic is

Where and

x	(x-xbar)^2
47.3	16
39.3	16
40.3	9
38.3	25
46.3	9
43.3	0
42.3	1
49.3	36
40.3	9
46.3	9
433	130

Under Ho : mu = 40

The value of test statistic is

Alpha : level of significance = 0.01.

Since the test is right-tailed and value of test statistic is 2.7458. p-value is obtained by

Decision : Since p-value is greater than level of significance, we failed to reject Ho at 1% level of significance.

Initial Conclusion : There is not enough sufficient evidences support to claim that editor's claim is valid.

i.e. There is not sufficient evidence to claim that mean amount of nicotine in non filtered cigarettes is greater than 40 mg.

Final Conclusion : There is enough sufficient evidences support to claim that manufacturer's claim is valid.

i.e. There is sufficient evidence to claim that mean amount of nicotine in non filtered cigarettes is at most 40 mg.