Question

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.

8. 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?

Answer 1

It is specified that 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.

Let P = population proportion of low-income working families  

p = sample  proportion of low-income working families

Upper  limit of a confidence interval for P = p+zxSE(p)

Therefore it is specified that a limited amount of federal funds have been allocated to assist jurisdictions whose

P>4/5(p+zxSE(p))

If the confidence level is fixed, suppose it is 90% then z = 1.645

then P>4/5(p+1.645xSE(p)) and if it is compared with original P>(p+1.645xSE(p)) at 90% level wich leads to create benefit to the additional 1/5, that is 20% of the low income people and it creates additional burden allocating funds at a fixed confidence level say 90%.

On the other hand, if the confidence level is increased more than 90% and at which z>1.645 which results in increase in upper limit there by less number of people of low income will get the benefit and less allocation of funds which may become un-ethical and funds also may be miused.

To control the chances of un-ethical practice and misuse of funds and providing additional benefit to the 20% of the lower income group and not also getting additional burden for the funds, some what taking P>4/5(p+zxSE(p)) is better than taking P>(p+zxSE(p)) for confidence levels more than 90%.