Question

According to recent study, 166 of 493 technology CEOs from around the world responded that technological advances will transform their business and 88 responded that resource scarcity and climate change will transform their business. Complete parts (a) through (c) below. 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. ≤π≤ (Round to four decimal places as needed.)

Answer 1

To construct a 90% confidence interval estimate for the population proportion of CEO's who indicate technological advances will transform their business, we can use the formula: Confidence Interval = Point Estimate ± Margin of Error. The 90% confidence interval estimate is (0.3010, 0.3724).

Step-by-step explanation:

To construct a confidence interval for the population proportion of tech CEOs who indicate technological advances as one of the global trends that will transform their business, we can use the formula:

Confidence Interval = Point Estimate ± Margin of Error

where Point Estimate is the sample proportion and Margin of Error is the product of the critical value and the standard error. In this case, the sample proportion is 166/493 = 0.3367 (rounded to four decimal places). The critical value can be found using the z-table for a 90% confidence level, which is approximately 1.645. The standard error can be calculated using the formula √((p(1-p))/n), where p is the sample proportion and n is the sample size.

Plugging in the values, we get:

Margin of Error = 1.645 √((0.3367(1-0.3367))/493) ≈ 0.0357

Therefore, the 90% confidence interval estimate for the population proportion is 0.3367 ± 0.0357, or (0.3010, 0.3724) (rounded to four decimal places).