As a condition of employment Fashion Industries applicants m

As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 290 applicants, 26 failed the test. (Use Student\'s z Distribution Table.)

Develop a 98% confidence interval for the proportion of applicants that fail the test. (Round your answers to 3 decimal places.)

Solution

A)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.089655172          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.016776125          
              
Now, for the critical z,              
alpha/2 =   0.01          
Thus, z(alpha/2) =    2.33          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.050566802          
upper bound = p^ + z(alpha/2) * sp =    0.128743543          
              
Thus, the confidence interval is              
              
(   0.050566802   ,   0.128743543   ) [ANSWER]

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No, as some of the interval is less than 11%. [ANSWER]