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 19.2mg and a standard deviation of 3.22 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?   1. What is the test statistic? 2. What is the p-value?

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 19.2mg and a standard deviation of 3.22 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?
 
1. What is the test statistic?
2. What is the p-value?

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