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. 1. 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. 2. 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.) 3. 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. 4. Provide an appropriate statistical interpretation of the 90% confidence interval found in number 7. 5. 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%? 6. 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.
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.
1. Describe in two or three sentences how a simple random
2. A researcher reported that a sample of size n=30 produced a sample
3. 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.
4. Provide an appropriate statistical interpretation of the 90% confidence interval found in number 7.
5. 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%?
6. 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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