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Cybersecurity survey. Refer to the State of Cybersecurity (2015) survey of firms from around the world, Exercise 1.201.20 (p. 26). Recall that of the 766 firms that responded to the survey, 628 (or 82%82 \% ) expect to experience a cyberattack (e.g., a Malware, hacking, or phishing attack) during the year. Estimate the probability of an expected cyberattack at a firm during the year with a 90%90 \% confidence interval. Explain how 90%90 \% is used as a measure of reliability for the interval.

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Given:

n=Sample size=766x=Number of successes=628c=Confidence coefficient=90%=0.90\begin{aligned} n&=\text{Sample size}=766 \\ x&=\text{Number of successes}=628 \\ c&=\text{Confidence coefficient}=90\%=0.90 \end{aligned}

We need to determine a confidence interval about the population proportion pp.

The confidence interval about the population proportion is p^±E\hat{p}\pm E with E=zα/2p^q^nE=z_{\alpha/2}\cdot \sqrt{\dfrac{\hat{p}\hat{q}}{n}}.

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