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 addresses the original claim. 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 19.4 mg and a standard deviation of 3.52 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?

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha=0.05

test statistic t= xbar-mean/s/sqrt(n)

t= 19.4-21.1/3.52/sqrt(25)

t= -1.7/3.52/5

t= -1.7/0.704

t= -2.41

degrees of freedom= n-1=25-1=24

The P-Value is .011989. The result is NOT significant because p > .05.

Decision: REJECT NULL HYPOTHESIS H0.

Conclusion: We have sufficient evidence to conclude that the mean tar content of filtered 100 mm cigarettes is less than 21.1 ​mg. Result suggests that filler is effective.