Respuesta :
Answer:
[tex]0.192 - 1.645\sqrt{\frac{0.192(1-0.192)}{250}}=0.151[/tex]
[tex]0.192 + 1.645\sqrt{\frac{0.192(1-0.192)}{250}}=0.233[/tex]
Step-by-step explanation:
Information given
[tex]X= 48[/tex] number of people who rent their home
[tex]n= 250[/tex] represent the sample size
[tex]\hat p =\frac{48}{250}= 0.192[/tex] represent the proportion of people who rent their home
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=\pm 1.645[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
If we replace the values obtained we got:
[tex]0.192 - 1.645\sqrt{\frac{0.192(1-0.192)}{250}}=0.151[/tex]
[tex]0.192 + 1.645\sqrt{\frac{0.192(1-0.192)}{250}}=0.233[/tex]
