What are the global trends that technology CEOs believe will transform their bus

Question

What are the global trends that technology CEOs believe will transform their business? According to a PwC white paper, 105 of 117 technology CEOs from around the world responded that technological advances will transform their business and 42 responded that resourse scarcity and climate change will transform their business.

a. Cosntruct a 95% 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 95% confidence interval estimate for the population proportion of CEOs who indicate resource scarcity and climate change as one of the global trends that will transform their business.

c. Interpret the intervals in (a) and (b)

Explanation / Answer

a)
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=105
Sample Size(n)=117
Sample proportion = x/n =0.897
Confidence Interval = [ 0.897 ±Z a/2 ( Sqrt ( 0.897*0.103) /117)]
= [ 0.897 - 1.96* Sqrt(0.001) , 0.897 + 1.96* Sqrt(0.001) ]
= [ 0.842,0.952]

b)
Mean(x)=42
Sample Size(n)=117
Sample proportion = x/n =0.359
Confidence Interval = [ 0.359 ±Z a/2 ( Sqrt ( 0.359*0.641) /117)]
= [ 0.359 - 1.96* Sqrt(0.002) , 0.359 + 1.96* Sqrt(0.002) ]
= [ 0.272,0.446]

c)
Interpretations:
1) We are 95% sure that the interval [ 0.842,0.952] contains the true proportion of people responded that technological advances will transform their business

1) We are 95% sure that the interval [ 0.272,0.446] contains the true proportion of people responded that resourse scarcity and climate change will transform their business

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