Question

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.

• Provide a definition of a simple random sample. Describe by using two or three sentences how a simple random sample of size n=20 could be obtained from the full list of jurisdictions using either random numbers alone or a systematic sampling method.

• A researcher reported that an obtained sample of size n=20 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 percent of low-income working families. Along with the upper and lower limits that make up the confidence interval, provide a statement justifying the critical value used in the calculation of the margin of error. (Round the limits to two decimal places.)

• Express an appropriate statistical interpretation of the 90% confidence interval you found in number 6. Provide an explanation as to why it would be very unlikely that a different sample would produce the same confidence interval.

• If a limited amount of federal funds have been allocated to assist jurisdictions whose percent of low-income working families exceeds a threshold set at 4/5 of 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 argues for funds based on a confidence interval provided by his/her campaign supporters, would this raise any ethical concerns, or constitute a misuse of statistics, or both? Why or why not?

Reference(s): The Working Poor Families Project. (2011). Indicators and Data. Retrieved from http://www.workingpoorfamilies.org/indicators/

2011 Data
Jurisdiction	Percent of low income working families (<200% poverty level)	Percent of 18-64 year olds with no HS diploma
Alabama	37.3	15.3
Alaska	25.9	8.6
Arizona	38.9	14.8
Arkansas	41.8	14
California	34.3	17.6
Colorado	27.6	10.1
Connecticut	21.1	9.5
Delaware	27.8	11.9
District of Columbia	23.2	10.8
Florida	37.3	13.1
Georgia	36.6	14.9
Hawaii	25.8	7.2
Idaho	38.6	10.7
Illinois	30.4	11.5
Indiana	31.9	12.2
Iowa	28.8	8.1
Kansas	32	9.7
Kentucky	34.1	13.6
Louisiana	36.3	16.1
Maine	30.4	7.1
Maryland	19.5	9.7
Massachusetts	20.1	9.1
Michigan	31.6	10
Minnesota	24.2	7.3
Mississippi	43.6	17
Missouri	32.7	11.1
Montana	36	7
Nebraska	31.1	8.7
Nevada	37.4	16.6
New Hampshire	19.7	7.3
New Jersey	21.2	10.1
New Mexico	43	16.2
New York	30.2	13
North Carolina	36.2	13.6
North Dakota	27.2	5.9
Ohio	31.8	10.3
Oklahoma	37.4	13.2
Oregon	33.9	10.8
Pennsylvania	26	9.4
Rhode Island	26.9	12
South Carolina	38.3	14.2
South Dakota	31	8.7
Tennessee	36.6	12.7
Texas	38.3	17.8
Utah	32.3	9.9
Vermont	26.2	6.6
Virginia	23.3	10.2
Washington	26.4	10.2
West Virginia	36.1	12.9
Wisconsin	28.7	8.5
Wyoming	28.1	8

Answer 1

Only the first two questions answered.

Provide a definition of a simple random sample. Describe by using two or three sentences how a simple random sample of size n=20 could be obtained from the full list of jurisdictions using either random numbers alone or a systematic sampling method.

A simple random sample is a part of a the population in which each observation of the sample has an equal probability of being chosen into the sample.

steps to simple random sample
- Provide a serial number to each observation in the jurisdiction data.
- Using random number generator, generate n= 20 (n is as per sample needed) number lying between 1 and the maximum number of entries in the data.
- Now pick the observation according to the random number generated.

A researcher reported that an obtained sample of size n=20 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 percent of low-income working families. Along with the upper and lower limits that make up the confidence interval, provide a statement justifying the critical value used in the calculation of the margin of error. (Round the limits to two decimal places.)

Express an appropriate statistical interpretation of the 90% confidence interval

If multiple samples of n =20 is taken from the data provided, 90% of times the mean of the samples will lies in the interval mentioned above.

We are 90% confident that the true mean the population is contained in the interval provided above.