Question

If n = 580 and X = 464, construct a 90% confidence interval for the population proportion, p.

Answer 1

Answer:

$0.80 - 1.64 \sqrt{\frac{0.8(1-0.8)}{580}}=0.773$

$0.80 + 1.64 \sqrt{\frac{0.8(1-0.8)}{580}}=0.827$

And the 90% confidence interval would be given (0.773;0.827).

Step-by-step explanation:

The information given is:

$X = 464$ represent the number of individuals with the characteristic

$n = 580$ the sample size

$\hat p =\frac{X}{n}= \frac{464}{580}= 0.8$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 90% confidence interval the value of $\alpha=1-0.9=0.1$ and $\alpha/2=0.05$, the critical value for this case is:

$z_{\alpha/2}=1.64$

And replacing into the confidence interval formula we got:

$0.80 - 1.64 \sqrt{\frac{0.8(1-0.8)}{580}}=0.773$

$0.80 + 1.64 \sqrt{\frac{0.8(1-0.8)}{580}}=0.827$

And the 90% confidence interval would be given (0.773;0.827).