Mathematics: In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ( Autism and developmental, 2008). Find the proportion of ASD in Arizona with a confidence level of 99%.

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In 2008, there were 507 children in Arizona out of

erickamiles1797

08.02.2022

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:

$x=507\\n=32601\\\text{Confidence level }=99\%$

The sample proportion is:

$\hat p=\frac{x}{n}=\frac{507}{32601}=0.016$

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:

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

$=0.016\pm 2.58\cdot\sqrt{\frac{0.016(1-0.016)}{32601}}\\\\=0.016\pm 0.0018\\\\=(0.0142, 0.0178)\\\\\approx (0.014, 0.018)$

Thus, the 99% confidence interval for the proportion of ASD in Arizona is (0.014, 0.018).

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