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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 19.6 mg and a standard deviation of 3.68 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 do the results suggest, if anything, about the effectiveness of the filters?

Respuesta :

aramisdegaula1977

Answer:

There is sufficient statistical evidence in the sample to state that the average tar content in filter cigarettes is less than 21.1.

Step-by-step explanation:

To solve this problem, we run a hypothesis test about the population mean. Consider the average tar content in filter cigarettes.

Mean in the null hypothesis (Mo) =

Sample size (n) = 25

Sample mean (X) = 19.6

Sample standard deviation (S) = 3.68

Significance level = 0.05

H0: Mo = 21.1

Ha: Mo = <21.1

Test statistic = [tex]\frac{(X - Mo)\sqrt{n}}{s}[/tex]

Left critical T value (for 0.05) = -1.7109

Calculated statistic = [tex]\frac{(19.6 - 21.1)\sqrt{25}}{3.68}[/tex] = -2.0380

Since, the value of the test statistic is less than the value of the calculated statistic, the null hypothesis is rejected. There is sufficient statistical evidence in the sample to state that the average tar content in filter cigarettes is less than 21.1.

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