Assume that a simple random sample has been selected from a

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 18.8 mg and a standard deviation of 3.83mg. 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?

Solution

Let x be a random variable that represents tar contents of 100 mm cigarettes.
random sample size, n = 25
sample mean, x-bar = 18.8 and
sample standard deviation, s = 3.83

Hypotheses:
Null: Ho: ? = 21.1
Alternative : Ha : ? < 21.1 (CLAIM)

Test to be used: left-tailed t-test

Test statistic: t-score = [x-bar - ? ] / ( s/?n)
= [18.8