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%.
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 cha...
In 2011, the national percent of low-income working families had an approximately normal distribution with a mean of 31.3% and a standard deviation of 6.2% (The Working Poor Families Project, 2011). Although it remained slow, some politicians claimed that the recovery from the Great Recession was steady and noticeable. As a result, it was believed that the national percent of low-income working families was significantly lower in 2014 than it was in 2011. To support this belief, a spring 2014...
Part 3: Hypothesis Testing In 2011, the national percent of low-income working families had an approximately normal distribution with a mean of 31.3% and a standard deviation of 6.2% (The Working Poor Families Project, 2011). Although it remained slow, some politicians claimed that the recovery from the Great Recession was steady and noticeable. As a result, it was believed that the national percent of low-income working families was significantly lower in 2014 than it was in 2011. To support this...