A study showed 120 eases of blue lung disease among 1000 ins

A study showed 120 eases of \"blue lung disease\" among 1000 instructors who used dry erase markers in classes and 90 eases of \"blue lung disease\" among 1000 instructors who did not use dry erase markers in classes. Test whether instructors who used dry erase markers in classes were significantly more likely to develop blue lung disease\" than instructors who did not use dry erase markers in classes. State the mill and alternative hypotheses associated with the test. What is the calculated value of the associated test statistic? What is the p-VALUE for the test (please use FOUR decimal places)? If alpha = 0.05, state your decision regarding the null hypothesis by comparing alpha to the p-VALUL. State your conclusion (meaning, describe what the decision means in this problem).

Solution

a)

Let p1 = proportion of those who use dry erase markers in class with blue lung disease

p2 = proportion of those who do not use dry erase markers in class with blue lung disease

Formulating the hypotheses          
Ho: p1 - p2   <=   0  
Ha: p1 - p2   >   0   [ANSWER]

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

b)

Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.12      
p2 = x2/n2 =    0.09      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.013693064      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    2.19089023   [ANSWER]

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

c)  
          
          
Also, the p value is, as this is right tailed,          
          
P =    0.014229868   [ANSWER]  
          
***************

d)

As

P < 0.05, we Reject Ho. [ANSWER]

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

e)

Thus, there is significant evidence that instructors who used dry erase markers in classes are more likely to develop \"blue lung disease\" than instructors who did not use dry erase markers in classes.