Answer:
a) 0.567
b) (0.5414,0.5926)
c) (0.5364,0.5976)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 1007
Number of respondent that they will be able to afford health insurance in the future, x = 571
a) point estimate of the population proportion
[tex]\hat{p} = \displaystyle\frac{x}{n} = \frac{571}{1007} = 0.567[/tex]
b) 90% Confidence Interval.
[tex]\hat{p} + z_{\text{critical}}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.10} = \pm 1.64[/tex]
Putting values, we get,
[tex]0.567 \pm 1.64\times \sqrt{\dfrac{0.567(1-0.567)}{1007}}\\\\0.567 \pm 0.0256=(0.5414,0.5926)[/tex]
c) 95% Confidence Interval.
[tex]\hat{p} + z_{\text{critical}}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96[/tex]
Putting values, we get,
[tex]0.567 \pm 1.96\times \sqrt{\dfrac{0.567(1-0.567)}{1007}}\\\\0.567 \pm 0.0306=(0.5364,0.5976)[/tex]
