Answered: Suppose you are interested in the rate…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Suppose you are interested in the rate of autism among current school-aged children in Utah. You collect a sample of 400 children between the ages of 5 and 18 and find that two have had a previous diagnosis of an autism disorder. You plan to calculate a 95% confidence interval estimator of the proportion of school-aged children in Utah who have ever had a diagnosis of an autism disorder.

Which of the following is the most likely reason you would use a Wilson estimator to calculate the confidence interval estimator?

A confidence interval estimator based on the Wilson estimator does not use the normal distribution.

It is possible that if even the actual proportion in Utah is 1%, your sample may only have very few children who have had a previous diagnosis of an autism disorder.

It is an easier way to calculate the confidence interval estimator.

It is uncomfortable to define having been diagnosed with autism as a success.

Let p be the proportion of school-aged children in Utah who have ever had a diagnosis of an autism disorder. Using the Wilson estimate, the 95% confidence interval estimate of p is0.0099 ± . (Hint: For a 95% confidence interval estimate, use zα/2zα/2 = 1.96.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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