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telo118 [61]
3 years ago
9

A study showed that 14 of 180 publicly traded business services companies failed a test for compliance with Sarbanes-Oxley requi

rements for financial records and fraud protection. Assuming that these are a random sample of all publicly traded companies, construct a 95% confidence interval for the overall noncompliance proportion. (Round your answers to 4 decimal places.)
Mathematics
1 answer:
Vika [28.1K]3 years ago
4 0

Answer:

The 95% confidence interval for the overall noncompliance proportion is (0.0387, 0.1169).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 180, \pi = \frac{14}{180} = 0.0778

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0778 - 1.96\sqrt{\frac{0.0778*0.9222}{180}} = 0.0387

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0778 + 1.96\sqrt{\frac{0.0778*0.9222}{180}} = 0.1169

The 95% confidence interval for the overall noncompliance proportion is (0.0387, 0.1169).

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