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 and alternative hypothesis, test stastitic, P-value and state the final conclusion that addresses the original claim.

a simple random sample of 25 filtered 100mm cugarettes is obtained and and the tar content of each cigarettes is measured. The sample has a mean of 20.2mg and a standard deviation of 3.59mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100mm cigarettes is less than 21.1, which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything about the effectiveness of the filters.

A. fail to reject the Ho. There is insufficient evidence to support the claim that the mean tar content of filtered 100mm cigarettes is less than 21.1.

B. fail to reject Ho. There is sufficient evidence to support the claim that the mena tar content of filtered 100mm cigarettes is less than 21.1mg

C. Reject Ho. There is sufficient evidence to support the claim that the mean tar content of filtered 100mm cigarettes is less than 21.1mg

D. reject Ho. There is insufficient evidence to support the claim that he mwan tar content of filtered 100mm cigarettes is less than 21.1

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   21.1  
Ha:    u   <   21.1  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    24          
tcrit =    -   1.71088208      
              
Getting the test statistic, as              
              
X = sample mean =    20.2          
uo = hypothesized mean =    21.1          
n = sample size =    25          
s = standard deviation =    3.59          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.253481894          
              
Also, the p value is              
              
p =    0.111052181          
              
As P > 0.05, we fail to reject the null hypothesis.

Hence,

OPTION A. fail to reject the Ho. There is insufficient evidence to support the claim that the mean tar content of filtered 100mm cigarettes is less than 21.1. [ANSWER, A]