In: Statistics and Probability
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
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]