Answer:
[tex]0.225 - 1.64 \sqrt{\frac{0.225(1-0.225)}{280}}=0.184[/tex]
[tex]0.225 + 1.64 \sqrt{\frac{0.225(1-0.225)}{280}}=0.266[/tex]
And the best option would be:
a. (0.184, 0.266)
Step-by-step explanation:
We have the following info given:
[tex] X= 63[/tex] represent the homeless persons that were veterans
[tex] n= 280[/tex] represent the sampel size
The estimated proportion for this case would be:
[tex]\hat p=\frac{63}{280}= 0.225[/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], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=1.64[/tex]
And replacing into the confidence interval formula we got:
[tex]0.225 - 1.64 \sqrt{\frac{0.225(1-0.225)}{280}}=0.184[/tex]
[tex]0.225 + 1.64 \sqrt{\frac{0.225(1-0.225)}{280}}=0.266[/tex]
And the best option would be:
a. (0.184, 0.266)
