Question

As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 210 applicants, 24 failed the test. (1)Develop a 90% confidence interval for the proportion of applicants that fail the test. (Round your answers to 3 decimal places.) For the applicants, the confidence interval is between ____ and ____. (2) Would it be reasonable to conclude that more than 7% of the applicants are now failing the test? Yes or No.

Answer 1

The total no of observation are = N = 210

failed applicants = 24

the proportion of applicants failed a drug test = p^ = 24/210

= 0.1143

so proportion mean = p^ = 0.1143

Variance = p^(1-p^)

= 0.1013

90 % Confidence interval that sample mean falls within 2 standard errors of the population mean

so confidence interval is,

[ sample mean ± 2 sample standard deviation / ?sample size ]

[ 0.1004 , 0.1283 ]

So,  For the applicants, the confidence interval is between 0.1004 and 0.1283

2) Yes,

Because the failing proportion mean is 11%

so it is very high than 7%

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