Suppose you have been hired by the Better Business Bureau (BBB) to investigate the settlement ratio of the complaints they have received. You plan to select a sample of n complaints to estimate the proportion of complaints the BBB is able to settle. We use p to denote the percentage or proportion of complaints settled among all the complaints that the BBB has received. Q1) Let’s apply the results above and derive some confidence intervals. Note that the population proportion p is unknown. In order to compute the standard error , we substitute for p. As long as the sample size n is sufficiently large, a normal distribution would approximate the sample distribution of the sample proportion well enough. Suppose the sample proportion you’ve found is 0.6. Find a 95% confidence interval of the population proportion, if the sample size is 36, 100, and 400, respectively. What effect does the sample size n have on the resulting confidence interval? Q2) It is often the case that we have a target for margin of error in mind and we want to know the sample size needed to guarantee such a margin of error when the confidence level is given. Use the formula to compute the sample sizes needed when the respective value of m is 1%, 3%, and 5% and the respective confidence level is 90%, 95%, and 99%.

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Description: Suppose you have been hired by the Better Business Bureau (BBB) to investigate the settlement ratio of the complaints they have received. You plan to select a sample of n complaints to estimate the proportion of complaints the BBB is able to settle.

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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Suppose you have been hired by the Better Business Bureau (BBB) to investigate the settlement ratio of the complaints they have received. You plan to select a sample of n complaints to estimate the proportion of complaints the BBB is able to settle. We use p to denote the percentage or proportion of complaints settled among all the complaints that the BBB has received.

Q1) Let’s apply the results above and derive some confidence intervals. Note that the population proportion p is unknown. In order to compute the standard error , we substitute for p. As long as the sample size n is sufficiently large, a normal distribution would approximate the sample distribution of the sample proportion well enough. Suppose the sample proportion you’ve found is 0.6. Find a 95% confidence interval of the population proportion, if the sample size is 36, 100, and 400, respectively. What effect does the sample size n have on the resulting confidence interval?

Q2)

It is often the case that we have a target for margin of error in mind and we want to know the sample size needed to guarantee such a margin of error when the confidence level is given. Use the formula to compute the sample sizes needed when the respective value of m is 1%, 3%, and 5% and the respective confidence level is 90%, 95%, and 99%.

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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