Question

According to recent study, 152 of 467 CEOs in a certain country are extremely concerned about Cyber threats, and 91

are extremely concerned about lack of trust in business. Complete parts (a) through (c) below.

a. Construct a 95% confidence interval estimate for the population proportion of CEOs in the country who are extremely concerned about cyber threats.

0.2830less than or equalspiless than or equals0.3680

b. Construct a 95% confidence interval estimate for the population proportion of CEOs in the country who are extremely concerned about lack of trust in business.

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(Round to four decimal places as needed.)

Answer 1

To construct a 95% confidence interval estimate for the population proportion of CEOs who are extremely concerned about cyber threats, we can use the formula CI = pˆ ± z * sqrt((pˆ * (1 - pˆ)) / n), where pˆ is the sample proportion, n is the sample size, and z is the z-score corresponding to the desired confidence level (in this case, 95%). The 95% confidence interval estimate for the population proportion of CEOs who are extremely concerned about cyber threats is approximately 0.2830 ≤ p ≤ 0.3680. The same process can be applied to estimate the proportion of CEOs who are extremely concerned about lack of trust in business, which is approximately 0.1570 ≤ p ≤ 0.2336.

Step-by-step explanation:

a. To construct a 95% confidence interval estimate for the population proportion of CEOs who are extremely concerned about cyber threats, we can use the formula:

CI = pˆ ± z * √((pˆ * (1 - pˆ)) / n)

Where pˆ is the sample proportion, n is the sample size, and z is the z-score corresponding to the desired confidence level (in this case, 95%).

Given that the study found 152 out of 467 CEOs are extremely concerned about cyber threats, the sample proportion is pˆ = 152/467 ≈ 0.3263. Using a standard normal distribution table, the z-score for a 95% confidence level is approximately 1.96. Plugging the values into the formula, we get:

CI = 0.3263 ± 1.96 * √((0.3263 * (1 - 0.3263)) / 467) ≈ 0.2830 ≤ p ≤ 0.3680

Therefore, the 95% confidence interval estimate for the population proportion of CEOs who are extremely concerned about cyber threats is approximately 0.2830 ≤ p ≤ 0.3680.

b. To construct a 95% confidence interval estimate for the population proportion of CEOs who are extremely concerned about lack of trust in business, we can follow the same steps as in part (a), but using the given information that 91 out of 467 CEOs are extremely concerned about lack of trust in business. The sample proportion is pˆ = 91/467 ≈ 0.1953. Using the z-score for a 95% confidence level, the formula becomes:

CI = 0.1953 ± 1.96 * √((0.1953 * (1 - 0.1953)) / 467) ≈ 0.1570 ≤ p ≤ 0.2336

Therefore, the 95% confidence interval estimate for the population proportion of CEOs who are extremely concerned about lack of trust in business is approximately 0.1570 ≤ p ≤ 0.2336.