Fashion Industries randomly tests its employees throughout t

Fashion Industries randomly tests its employees throughout the year. Last year in the 440 random tests conducted, 22 employees failed the test. (Use z Distribution Table.)

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

Confidence interval is between ____and____ .

2. Would it be reasonable to conclude that less than 5% of the employees are not able to pass the random drug test? No Yes

Solution

1.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.05          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.010390118          
              
Now, for the critical z,              
alpha/2 =   0.01          
Thus, z(alpha/2) =    2.326347874          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.025828972          
upper bound = p^ + z(alpha/2) * sp =    0.074171028          
              
Thus, the confidence interval is              
              
(   0.025828972   ,   0.074171028   ) [ANSWER]

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2.

NO, as part of the interval is greater than 0.05. [ANSWER, NO]