Help to both A & B Please? Statistics?

Fourteen of 180 publicly traded business services companies failed a test for compliance with Sarbanes-Oxley requirements for financial records and fraud protection.

A. Assuming that these are a random sample of all publicly traded companies, construct a 95 percent confidence interval for the overall noncompliance proportion.

B. Why might this statistic not apply to all sectors of publicly traded companies? (e.g. aerospace and defense)

A).
Let p be the true proportion of all publicly traded companies who failed a test for compliance. Then let ^p to denote the sample proportion of all publicily traded companies for non-compliance.

In this case,
n = 180.
^p = The sampled proportion of this random selected sample = 14/180 = 0.0778
The coefficient of confidence = 95%
i.e. (1 - 鈭?% = 95%
1 - 鈭?= 0.95
鈭?= 0.05

Since both n^p = 180 * (14/180) = 14 and n(1-^p) = 180* [1-(14/180)] = 166 are both at least greater than 5, then n is considered to be large and it is appropriate to use the z distribution to estimate the true overall noncompliance proportion of all publicily traded companies, p in this case.

So, a 95% confidence interval for the overall noncompliance proportion
= [^p (+-) Z鈭?2 * 鈭歔^p(1-^p)/n]
= [0.0778 (+-) z(0.05/2) * 鈭歔0.0778(1-0.0778)/180]
= [0.0778 (+-) z0.025 * 鈭歔0.0778(1-0.0778)/180]
= [0.0778 (+-) 1.96 * 鈭歔0.0778(1-0.0778)/180]
= [0.0778 (+-) 0.01996]
= [0.05784, 0.09776]
or
= [5.784%, 9.776%]

B).
Because this static is calculated based on a random sample of business services sector of publicly traded companies only.