Question

In: Statistics and Probability

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A...

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 equals n=951 and x equals x=543 who said​ "yes." Use a 90% confidence level.

b) Identify the value of the margin of error E.

E=

c) Construct the confidence interval

Solutions

Expert Solution

Note: parts a and d are not given in the question pasted.

We have the following sample information

n=951 is the sample size

is the sample proportion who said they felt vulnerable to identity theft.

The point estimate of population proportion who said they felt vulnerable to identity theft is 0.5710

The estimated standard error of proportions is

Since both are greater than 5, we can say that the sampling distribution of proportions is normal.

The significance level for 90% confidence is

the right tail critical value is

Using the standard normal table, we get for z=1.645, P(Z<1.645)=0.95

Hence,

b) Identify the value of the margin of error E.

ans: the value of the margin of error E=0.0264

c) Construct the confidence interval

The 90% confidence interval is

ans: the 90% confidence interval is [0.5446,0.5974]


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