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ad-work [718]
3 years ago
8

In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and de

velopmental," 2008). Find the proportion of ASD in Arizona with a confidence level of 99%.
Mathematics
1 answer:
Svetach [21]3 years ago
6 0

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:

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 <em>z</em> for 99% confidence level is, <em>z</em> = 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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