Respuesta :
Answer:
[tex]0.80 - 1.64 \sqrt{\frac{0.8(1-0.8)}{580}}=0.773[/tex]
[tex]0.80 + 1.64 \sqrt{\frac{0.8(1-0.8)}{580}}=0.827[/tex]
And the 90% confidence interval would be given (0.773;0.827).
Step-by-step explanation:
The information given is:
[tex]X = 464[/tex] represent the number of individuals with the characteristic
[tex]n = 580[/tex] the sample size
[tex]\hat p =\frac{X}{n}= \frac{464}{580}= 0.8[/tex]
The confidence interval would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 90% confidence interval the value of [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex], the critical value for this case is:
[tex]z_{\alpha/2}=1.64[/tex]
And replacing into the confidence interval formula we got:
[tex]0.80 - 1.64 \sqrt{\frac{0.8(1-0.8)}{580}}=0.773[/tex]
[tex]0.80 + 1.64 \sqrt{\frac{0.8(1-0.8)}{580}}=0.827[/tex]
And the 90% confidence interval would be given (0.773;0.827).
