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 100mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.4 mg and a standard deviation of 3.85 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100mm 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? Identify the P-value. The P-value is []. (Round to four decimal places as needed.) State the final conclusion that addresses the original claim. Choose the correct answer below. What do the results suggest, if anything. about the effectiveness of the filters?

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   21.1  
Ha:    u   <   21.1  
              
As we can see, this is a    left   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    19.4          
uo = hypothesized mean =    21.1          
n = sample size =    25          
s = standard deviation =    3.85          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.207792208          
              
Thus, the p value is              
              
p =    0.013629381   [ANSWER]

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b)      
              
As P < 0.05, we reject Ho.

Thus, it is OPTION B. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. [ANSWER, B]

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c)

OPTION D: The results suggest that the filters are effective. [ANSWER, D]