Question

12 A study showed that 14 of 180 publicly traded business services companies failed a test for compliance with Sarbanes-Oxley requirements 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.) 2. points The 95% confidence interval is from 0.0390 x to 0.117

Answer 1

Solution :

Given that,

Point estimate = sample proportion = $\hat p$ = x / n = 14 / 180 = 0.078

1 - $\hat p$ = 1 - 0.078 = 0.922

Z_$\alpha$/2 = 1.96

Margin of error = E = Z_{$\alpha$ / 2} * $\sqrt$ (($\hat p$ * (1 - $\hat p$ )) / n)

= 1.96 * ($\sqrt$((0.078 * 0.922) / 180)

Margin of error = E = 0.0392

A 95% confidence interval for population proportion p is ,

$\hat p$ - E < p < $\hat p$ + E

0.078 - 0.0392 < p < 0.078 + 0.0392

0.0388 < p < 0.117

The 95% confidence interval is from : 0.0388 to 0.117