Suppose you would like to know if there is a difference between the proportion o

Question

Suppose you would like to know if there is a difference between the proportion of male TLU undergaduate students who use tobacco and the proportion of female TLU undergraduate students who use tobacco. Of the 206 males who filled out a questionaire a the beggining of the term, 60 answered "yes" to the questions, "do you smoke cigarrettes or chew tobacco?" Total of females who filled out a questionaire was 262. Assuming that the students who filled out questionaire at the beggining of the term are a random sample of TLU undergraduates. Note that p-hat = .25

b. With 95% confidence, find the margin of error.

c. Construct a 95% confidence interval for the difference of true proportion of male and female.

Explanation / Answer

Hi! I am assuming that p-hat is the sample proportion for females, as that part is not given.

a)

Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.291262136      
p2^ = x2/n2 =    0.25      

Hence,

p1^ - p2^ = 0.041262136 [ANSWER]

***************************

b)
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.041445494      
          
For the   95%   confidence level, then  
          
alpha/2 = (1 - confidence level)/2 =    0.025      
z(alpha/2) =    1.959963985      

Margin of error = z(alpha/2)*sd =    0.081231676 [ANSWER]

**************************

c)

Also,
      
lower bound = p1^ - p2^ - z(alpha/2) * sd =    -0.03996954      
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.122493811      
          
Thus, the confidence interval is          
          
(   -0.03996954   ,   0.122493811 ) [ANSWER]

************************

D)

As the interval includes 0, no, we do not reject Ho. [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.