Suppose the proportion of all Canadians who have used mariju

Suppose the proportion of all Canadians who have used marijuana in the past 6 months is p = 0.40. In a group of 200 Canadians that are representative of all Canadians, would it beunusual for the proportion who have used marijuana in the past 6 months to be less than 0.32?

Solution

Here, the mean of the proportions is

u = 0.40

and standard deviation of

sigma = sqrt(p(1-p)/n) = sqrt(0.40*(1-0.40)/200) = 0.034641016

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.32      
u = mean =    0.4      
          
s = standard deviation =    0.034641016      
          
Thus,          
          
z = (x - u) / s =    -2.309401087      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2.309401087   ) =    0.010460667 [ANSWER]

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It depends on how you define unusual in class. Some classes define it as P < 0.1, in which case, this one is unusual. However, please use the standard you use in class.