Question

According to recent​ study,149 of 480 CEOs in a certain country are extremely concerned about Cyber​ threats, and 75 are extremely concerned about lack of trust in business. Complete parts​ (a) through​ (b) below.

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

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.

Answer 1

Solution :

a) Given that, for cyber threats : x = 149 , n = 480

=> p = x/n

= 149/480

= 0.3104

=> q = 1 - p = 0.6896

=> for 95% confidence interval, Z = 1.96

=> The 95% confidence interval of the population proportion of CEOs in the country who are extremely concerned about cyber threats is

=> p +/- Z*sqrt(p*q/n)

=> 0.3104 +/- 1.96*sqrt(0.3104*0.6896/480)

=> 0.2690 < p < 0.3518

b)
Given that, for lack of trust in business : x = 75 , n = 480

=> p = x/n

= 75/480

= 0.1563

=> q = 1 - p = 0.8437

=> for 95% confidence interval, Z = 1.96

=> The 95% confidence interval of the population proportion of CEOs in the country who are extremely concerned about lack of trust in business is

=> p +/- Z*sqrt(p*q/n)

=> 0.1563 +/- 1.96*sqrt(0.1563*0.8437/480)

=> 0.1238 < p < 0.1888