Four part question Use the sample data and confidence level given below to compl

Question

Four part question

Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n =980 and x =530 who said "yes." Use a .90% confidence level.

a) Find the best point estimate of the population proportion p. Round to three decimal

b) Identify the value of the margin of error E. Round to four decimal

c) Construct the confidence interval. ___

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

1. 90 % of sample proportions will fall between the lower bound and the upper

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

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

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

Explanation / Answer

a.
No. of success(x)=530
Sample Size(n)=980
best point estimate of the population proportion p = Sample proportion = x/n =0.54082
b.
Margin of Error = 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)=530
Sample Size(n)=980
Sample proportion =0.54082
Margin of Error = Z a/2 * ( Sqrt ( (0.5408*0.4592) /980) )
= 1.645* Sqrt(0.00025)
=0.02619
c.
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
Confidence Interval = [ 0.54082 ±Z a/2 ( Sqrt ( 0.54082*0.45918) /980)]
= [ 0.54082 - 1.645* Sqrt(0.00025) , 0.5408 + 1.65* Sqrt(0.00025) ]
= [ 0.51463,0.56701]
d.
3. There is a 90 % chance that the true value of the population proportion will falll between the lower bound and the upper bound.

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