Answer to Question #345170 in Statistics and Probability for Zyrille San Juan

Question

p=0.64

a=0.05

n=180

what is the point estimate of p?

what is the interval estimate of p?

Answer 1

a)

The point estimate of $p$ is $p=0.64$

b)

The critical value for $\alpha = 0.05$ is $z_c = z_{1-\alpha/2} = 1.96.$

The corresponding confidence interval is computed as shown below:

$$CI=(\hat{p}-z_c\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+z_c\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})$$

$$=(0.64-1.96\sqrt{\dfrac{0.64(1-0.64)}{180}},$$

$$0.64+1.96\sqrt{\dfrac{0.64(1-0.64)}{180}})$$

$$=(0.57, 0.71)$$

Therefore, based on the data provided, the 95% confidence interval for the population proportion is $0.57 < p < 0.71,$ which indicates that we are 

95% confident that the true population proportion $p$  is contained by the interval $(0.57, 0.71).$