Answered: A pool of 500 Houston residents…

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

A pool of 500 Houston residents indicated that 16% of them participated in Women’s March on January 21, 2017. We are interested in figuring out the actual percentage of Houston residents that participated in Women’s March. Please answer the following questions.

1. For each sample of size 500 taken from the population, a sample proportion (pbar) can be calculated. If we were able to collect all possible samples of 500 from the population and obtain all sample proportions (pbar’s), what is the distribution of all sample proportions called? Describe the shape of this distribution.

Group of answer choices

normal distribution (bell shape)

non-normal distribution

2. Given that the sample proportion is 16% (pbar = .16) and the population proportion (p) is unknown, what is your best guess of the population proportion (p)?

My best guess is that the population proportion is more than 16%.

My best guess is that the population proportion is less than 16%.

My best guess is that the population proportion is close to 16%.

3.ince the true population proportion (p) is unknown, we would approximate it by sample proportion (pbar). Now assume p = pbar = 0.16.

What is the center (i.e., the mean) and the spread (i.e., the standard error) of this distribution?

Hint: Use the Central Limit Theorem’s result on the sampling distribution of sample proportion. You may also need to justify why CLT is applicable here.

We can use CLT here because 500 × 16% > 10, and 500 × (1-16%) > 10. The center is at 16%, and the spread is 1.6395%

We can use CLT here because 500 × 16% > 10, and 500 × (1-16%) > 10. The center is at 16%, and the spread is also at 16%.

We can use CLT here because 500 × 16% > 10, and 500 × (1-16%) > 10. The center is at 16%, and the spread is 0.02688%

CLT does not apply here because sample size is too small.

4. Since the true population proportion (p) is unknown, we would approximate it by sample proportion (pbar). Now assume p = pbar = 0.16.

What is the probability that the sample proportion will be within 5% of the true population proportion? Hint: To find probability (p – .05 < pbar < p + .05).

The probability is between 30% and 60%

The probability is more than 90%

The probability is between 60% and 90%

The probability is between 0% and 30%

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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