Use the sample data and confidence level given below to complete the following q

Question

Use the sample data and confidence level given below to complete the following questions: A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=941 and x=525. Use a 90% confidence level.

Questions:

a) Find the best point estimate of the population proportion b (round to 3 decimal places as needed)

b) Identify the value of the margin of error E. E = ? (round to 3 decimal places as needed)

c) Construct the confidence interval. ? < p < ? (round to 3 decimal places as needed)

Explanation / Answer

Solution:- n = 941 , X = 525 , 90% confidence interval for Z = 1.645

a) p = X/n = 525/941 = 0.558 , q = 1-p = 1 - 0.558 = 0.442

b) margin of error E = Z * sqrt(pq/n) = 1.645*sqrt(0.558*0.442/941)
= 0.027

c) The confidence interval => p +/- E

= (0.558 - 0.027 , 0.558 + 0.027)

= (0.531 ,0.585)

=> the confidence interval 0.431 < p < 0.585.

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