If phat is equal to 073 then qhat is equal to In a study of

If phat is equal to 0.73, then qhat is equal to In a study of 100 new cars, 29 are white. Find phat and qhat, where phat is the proportion of new cars that are white. A recent study of 750 internet users in Europe found that 35% of internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the internet?

Solution

12.

qhat = 1 - phat = 0.27 [ANSWER]

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13.

phat = x/n = 29/100 = 0.29

Thus,

qhat = 1 - phat = 0.71 [ANSWER, B]

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14.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.35          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.017416467          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.315864351          
upper bound = p^ + z(alpha/2) * sp =    0.384135649          
              
Thus, the confidence interval is              
              
(   0.315864351   ,   0.384135649   ) [ANSWER, C]