Part 2: Confidence Intervals During the recovery from the Great Recession of 2007-2009, the economic situation for many families improved. However, in 2011 the recovery was slow and it was uncertain as to how much had really changed on the national level. To estimate the national average of the percent of low-income working families, a representative simple random sample of the percent of low-income working families from each of the country’s reporting jurisdictions could be used to calculate a point estimate and create a related confidence interval. With this confidence interval a better picture of the nation’s recovery can be had and legislative decisions can be made. Describe in two or three sentences how a simple random sample of size n=20 could be obtained from the full list of jurisdictions provided for use with this assignment. A researcher reported that a sample of size n=30 produced a sample mean of 32.56% and a sample standard deviation of 6.56%. Use this information to calculate a 90% confidence interval for the national average for the “percent of low-income working families”. Provide the upper and lower limits of the confidence interval and the margin of error. (Round the limits to two decimal places.) Provide an explanation as to why it would be very unlikely that a different sample of size n=30 would produce the same confidence interval. Provide an appropriate statistical interpretation of the 90% confidence interval found in number 7. If a limited amount of federal funds have been allocated to assist jurisdictions whose “percent of low-income working families” exceeds a threshold based on the upper limit of a confidence interval, what would be the effect of using a confidence level that is higher than 90%? If a public official requests funds based on a confidence interval provided by constituents in his/her district, would this raise any ethical concerns, or constitute a misuse of statistics, or both? Provide at least two sentences to respond to the situation presented.

Part 2: Confidence Intervals During the recovery from the Great Recession of 2007-2009, the economic situation for many families improved. However, in 2011 the recovery was slow and it was uncertain as to how much had really changed on the national level. To estimate the national average of the percent of low-income working families, a representative simple random sample of the percent of low-income working families from each of the country’s reporting jurisdictions could be used to calculate a point estimate and create a related confidence interval. With this confidence interval a better picture of the nation’s recovery can be had and legislative decisions can be made. Describe in two or three sentences how a simple random sample of size n=20 could be obtained from the full list of jurisdictions provided for use with this assignment. A researcher reported that a sample of size n=30 produced a sample mean of 32.56% and a sample standard deviation of 6.56%. Use this information to calculate a 90% confidence interval for the national average for the “percent of low-income working families”. Provide the upper and lower limits of the confidence interval and the margin of error. (Round the limits to two decimal places.) Provide an explanation as to why it would be very unlikely that a different sample of size n=30 would produce the same confidence interval. Provide an appropriate statistical interpretation of the 90% confidence interval found in number 7. If a limited amount of federal funds have been allocated to assist jurisdictions whose “percent of low-income working families” exceeds a threshold based on the upper limit of a confidence interval, what would be the effect of using a confidence level that is higher than 90%? If a public official requests funds based on a confidence interval provided by constituents in his/her district, would this raise any ethical concerns, or constitute a misuse of statistics, or both? Provide at least two sentences to respond to the situation presented.

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Description: Part 2: Confidence Intervals During the recovery from the Great Recession of 2007-2009, the economic situation for many families improved. However, in 2011 the recovery was slow and it was uncertain as to how much had really changed on the national

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Part 2: Confidence Intervals

During the recovery from the Great Recession of 2007-2009, the economic situation for many families improved. However, in 2011 the recovery was slow and it was uncertain as to how much had really changed on the national level. To estimate the national average of the percent of low-income working families, a representative simple random sample of the percent of low-income working families from each of the country’s reporting jurisdictions could be used to calculate a point estimate and create a related confidence interval. With this confidence interval a better picture of the nation’s recovery can be had and legislative decisions can be made.

Describe in two or three sentences how a simple random sample of size n=20 could be obtained from the full list of jurisdictions provided for use with this assignment.

A researcher reported that a sample of size n=30 produced a sample mean of 32.56% and a sample standard deviation of 6.56%. Use this information to calculate a 90% confidence interval for the national average for the “percent of low-income working families”. Provide the upper and lower limits of the confidence interval and the margin of error. (Round the limits to two decimal places.)

Provide an explanation as to why it would be very unlikely that a different sample of size n=30 would produce the same confidence interval.

Provide an appropriate statistical interpretation of the 90% confidence interval found in number 7.

If a limited amount of federal funds have been allocated to assist jurisdictions whose “percent of low-income working families” exceeds a threshold based on the upper limit of a confidence interval, what would be the effect of using a confidence level that is higher than 90%?

If a public official requests funds based on a confidence interval provided by constituents in his/her district, would this raise any ethical concerns, or constitute a misuse of statistics, or both? Provide at least two sentences to respond to the situation presented.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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