Answer:
The 99% confidence interval for the proportion of ASD in Arizona is (0.014, 0.018).
Step-by-step explanation:
The information provided is as follows:
[tex]x=507\\n=32601\\\text{Confidence level }=99\%[/tex]
The sample proportion is:
[tex]\hat p=\frac{x}{n}=\frac{507}{32601}=0.016[/tex]
The critical value of z for 99% confidence level is, z = 2.56.
Compute the 99% confidence interval for the proportion of ASD in Arizona as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.016\pm 2.58\cdot\sqrt{\frac{0.016(1-0.016)}{32601}}\\\\=0.016\pm 0.0018\\\\=(0.0142, 0.0178)\\\\\approx (0.014, 0.018)[/tex]
Thus, the 99% confidence interval for the proportion of ASD in Arizona is (0.014, 0.018).
