Use the sample data and confidence level given below to complete questions 2-5.

Question

Use the sample data and confidence level given below to complete questions 2-5.

A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1075 and x=501 who said “yes.” Use a 90% confidence level.

A) Find the best point estimate of the population proportion p (round to the nearest thousandths).

B) Identify the value of the margin of error E (round to the nearest ten thousandths).

C) Construct the confidence interval (lower limit < p < upper limit).

D) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

-90% of sample proportions will fall between the lower bound and upper bound.

-One has 90% confidence that the sample proportion is equal to the population proportion.

-There is a 90% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

-One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Explanation / Answer

A)here point estimate of the population proportion p =501/1075=0.466

B)std error =(p(1-p)/n)1/2 =0.0152

for 90% CI ; z =1.6449

hence value of the margin of error E =z*std error =0.0250

C) confidence interval =sample proportion -/+ margin of error =0.441 < p< 0.491

d)

-One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

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