Assume that a simple random sample has been selected from a normally distributed

Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that original claim. Use Minitab as necessary. 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 19.0 mg and a standard deviation of 3.50 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? What are the hypotheses? A. H_0: mu > 21.1 mg H_1: mu

Explanation / Answer

Hypothesis:

H0: mu > 21.1 mg
Ha: mu < 21.1 mg

Tests statistic:
n = 25 , x = 19 , s = 3.5 , mean = 21.1

t = ( x = mean)/( s/sqrt(n))
= ( 19 - 21.1) /( 3.5 /sqrt(25))
= -3
P value is calculated using t = -3, df = 24
P value = .003103.

Reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100mm cigarettes is less than 21.1 mg

The results suggest thst the filters are effective.

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