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

19.019.0

mg and a standard deviation of

3.143.14

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: = 21

Ha: < 21

Test statistics

t = - / S / sqrt(n)

= 19 - 21 / (3.14 / sqrt(25) )

= -3.18

This is test statistics value.

p-value for the test statistics of -3.18 and df of 24 = 0.0020 (From T table)

Since p-value < 0.05 level, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have sufficient evidence to support the claim.