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 19.0mg and a standard deviation of 3.45 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1mg, which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filters? Identify the test statistic.

Answer 1

Null Hypothesis

Alternative Hypothesis (Claim ) (Left tailed test)

Significance Level

Since population standard deviation is unknown, we use t test

Under H0, the test statistic is

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

The critical value of t for 24 df at 5% significance level is -1.711

The P-Value is .0028

Since p value is less than significance level. Reject H0.

Hence, we have enough evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1mg.