A practice of eighteen dentists upgraded their computer syst

A practice of eighteen dentists upgraded their computer system and suspects that in the process they lost information on recalls for many of their patients. They drew a simple random sample of two hundred patient records and discovered that twenty-two of those had follow-up calls that were not included in the new computer system. Use the =NORMDIST( ) function to determine the following:

a. The probability that the true proportion of missed follow-up calls is less than 10 percent among all records.

b. The probability that the true proportion of missed follow-up calls is greater than 20 percent among all records.

Solution

Here, the point estimate of the popultion proportion is

p^ = 22/200 = 0.11 (We treat this as the mean)

Then, the standard deviation of this is

sp = sqrt(p^ (1-p^)/n) = sqrt(0.11*(1-0.11)/200) = 0.022124647

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.1      
u = mean =    0.11      
          
s = standard deviation =    0.022124647      
          
Thus,          
          
z = (x - u) / s =    -0.451984612      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.451984612   ) =    0.325640034 [ANSWER]

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b)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.2      
u = mean =    0.11      
          
s = standard deviation =    0.022124647      
          
Thus,          
          
z = (x - u) / s =    4.067861512      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   4.067861512   ) =    0.0000237233 [ANSWER]