Answer:
(a) The best point estimate of the population proportion <em>p</em> is 0.51.
(b) The margin of error is 0.0299.
(c) The 95% confidence interval for population proportion of all respondent who said "yes" is (0.4801, 0.5399).
Step-by-step explanation:
The random variable <em>X</em> is defined as the number of respondents who felt vulnerable to identity theft.
The information provided is:
<em>n</em> = 1074
<em>x</em> = 543
(a)
A point estimate of a parameter is a distinct value used for the estimation the parameter. For instance, the sample mean is a point estimate of the population mean μ.
The best point estimate of the population proportion <em>p</em> is the sample proportion .
Compute the sample proportion value as follows:
Thus, the best point estimate of the population proportion <em>p</em> is 0.51.
(b)
The margin of error for the confidence interval of <em>p</em> is:
For 95% confidence level the critical value of <em>z</em> is:
Compute the margin of error as follows:
Thus, the margin of error is 0.0299.
(c)
Construct the 95% confidence interval for population proportion as follows:
Thus, the 95% confidence interval for population proportion of all respondent who said "yes" is (0.4801, 0.5399).