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 2525 filtered 100 mm cigarettes is​ obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.219.2 mg and a standard deviation of 3.353.35 mg. Use a 0.050.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.121.1 ​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

H0:Null Hypothesis:

HA: Alternative Hypothesis:

μ < 21.1

SE = s/

= 3.35/ = 0.67

Test statistic is:

t = (19.2 - 21.1)/0.67 = - 2.8358

ndf = 25 - 1 = 24

By Technology, P - value = 0.0046

Since P - Value is less than , the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.2 mg, which is the mean for unfiltered king size cigarettes.

The results suggest that the filters are effective.