Question

According to a recent study, 164 of 462 technology CEOs from around the world responded that technological advances will transform their business and 84 responded that resource scarcity and climate change will transform their business. Complete parts (a) through (b)

A. Construct a 90 confidence interval estimate for the population proportion of tech CEOs who indicate technological advances as one of the global trends that will transform their business.

B. Construct a 90 confidence interval estimate for the population proportion of tech CEOs who indicate resource scarcity and climate change as one of the global trends that will transform their business

Answer 1

A)

Sample proportion = 164 / 462 = 0.355

90% confidence interval for p is

- Z * Sqrt( ( 1 - ) / n) < p < + Z * Sqrt( ( 1 - ) / n)

0.355 -1.645 * sqrt( 0.355 * 0.645 / 462) < p < 0.355 +1.645 * sqrt( 0.355 * 0.645 / 462)

0.318 < p < 0.392

90% CI is ( 0.318 , 0.392)

B)

Sample proportion = 84 / 462 = 0.182

90% confidence interval for p is

- Z * Sqrt( ( 1 - ) / n) < p < + Z * Sqrt( ( 1 - ) / n)

0.182 -1.645 * sqrt( 0.182 * 0.818 / 462) < p < 0.182 +1.645 * sqrt( 0.182 * 0.818 / 462)

= 0.152 < p < 0.212

90% CI is (0.152 , 0.212)