During the recent recovery from the Great Recession of 2007-2009, the economic s

Question

During the recent recovery from the Great Recession of 2007-2009, the economic situation for many families has 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 population parameter of the percent of low-income working families, a representative simple random sample could be used to calculate a point estimate and a confidence interval. Write an appropriate sampling procedure that will enable a researcher to collect a simple random sample of size nr20 from the full list of jurisdictions. Carry out a sampling of the jurisdictions by using a random number generator, random number table, or the sampling capabilities of technology to select a simple random sample of size n = 20 from the full list of the jurisdictions. Provide the selected sample of 20 in the table included below, making sure to Include the corresponding percent of low-income working families (%LIWF) information for each jurisdiction selected. Use technology to calculate the sample mean and sample standard deviation of the percent of low-income working families for the selected 20 jurisdictions in your sample. Provide your mean and standard deviation and express in detail why it is unlikely that any two samples would produce the same results. A different sample of size n=20 produced a sample mean of 31.08% and a sample standard deviation of 5.48%. Use these values to calculate a 90% confidence interval (without the use of statistical technology) for the national mean percent of low-income working families. Please show all calculations and provide the upper and lower limits that make up the confidence interval. (Round the limits to two decimal places.) Express an appropriate statistical interpretation of the 90% confidence interval included in the answer to number 10. In any of the 20-value samples selected, some jurisdictions may have a percent of low-income working families that is not included in the 90% confidence interval calculated above. If federal funds are available only for jurisdictions whose percent of low-income working families falls within the reported confidence interval, explain whether an interval with a higher or lower confidence level would be more advantageous to the jurisdictions. If a lawmaker reports only research results that ensure that the jurisdiction he or she represents gets federal aid, explain whether such an action would constitute a misuse of statistics. If the

Explanation / Answer

Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but may include simple random sampling or systematic sampling.

A simple random sample is obtained by choosing elementary units in search a way that each unit in the population has an equal chance of being selected. A simple random sample is free from sampling bias. However, using a random number table to choose the elementary units can be cumbersome. If the sample is to be collected by a person untrained in statistics, then instructions may be misinterpreted and selections may be made improperly. Instead of using a least of random numbers, data collection can be simplified by selecting say every 10th or 100th unit after the first unit has been chosen randomly .such a procedure is called systematic random sampling.

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