A market survey is conducted by a provincial regulator to determine the proporti

Question

A market survey is conducted by a provincial regulator to determine the proportion of homeowners who would switch to a new internet service provided if they had the opportunity to do so. Of the 1 200 homeowners surveyed, 800 said that they would switch. 3 MARKS Estimate the value of the population proportion. Compute the standard error of the proportion. Construct a 99% confidence interval for the population proportion.

a)Estimate the value of the population proportion.

b)Compute the standard error of the proportion.

c)Construct a 99% confidence interval for the population proportion.

Explanation / Answer

Value of the population proportion = 800/1200=2/3

b) Standard error = Sqrt[p*(1-p)/n ] = sqrt[ 2/3*1/3 / 1200 ] =sqrt( 1/5400) = 0.0136

c) z for 99% confidence level is 2.575

Hence, the confidence interval is [ 0.66666 - 2.575*0.0136 , 0.66666 + 2.575*0.0136 ] =[0.63164,0.70168]

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