Question

I have this homework and i have to prepare a case study for it

 Develop a case study or scenario on a business/economics/related area problem.

 Collect and define a set of data on this scenario.

 Summarize and analyze the data set by using R-program, or Excel or SPSS.

 Apply at least five statistical data description techniques (descriptive measures),

 Then solve your case problems by using confidence intervals, determining sample size, hypothesis testing ( single population, two populations or more than two populations- considering different population parameters )

 Examine and compare output results obtained from statistical software package and write a conclusion.

 Write an executive report (including short story of the problem, data collection procedure, data structure, charts, analyses and solutions, conclusion and references).

Answer 1

The Topic I want to study is Personal Income of all 50 States of the United States in the years 2018. Learning about the current economic condition is the need of the hour. Choosing this subject provides data on exactly 50 pieces.

Since I am very curious to analyze the statistics for the country’s Income and improvement, I have collected the Personal Income [ in Millions of dollars] for the past two years 2018. My purpose to study this data is to check which states are getting a boost on Personal Income and which states still need consideration and funds from the government to improve its economy.

What is Personal Income by State?

The income people living in each state and the District of Columbia get from wages, proprietors' income, dividends, interest, rents, and government benefits. These statistics help assess and compare the economic well-being of state residents.

The data is collected from the website named Bureau of Economic Analysis which is an official website of the United States government. This data is collected by the Bureau of Economic Analysis from all the 50 States of the country. The link for the webpage is below:

https://www.bea.gov/data/income-saving/personal-income-by-state

When it comes to growth and development, we should start from the undeveloped areas by collecting the funds from the well- established states. That is why I am trying to study this data so that we can help our country understand what is the right place to put our money in to get a well-developed nation. For example, Some funds from the Top 5 Wealthy States can be given to the Top 5 Least developed states as this is not going to affect the Wealthy States that much as the least States will get a huge benefit from it.

Sample Data for the Personal Income of all 50 States of the United States is as follows:

State	Personal Income[Millions of Dollars]	Year
State	Personal Income[Millions of Dollars]
		2018
Connecticut		2,66,382
Maine		64,566
Massachusetts		4,83,657
New Hampshire		83,293
Rhode Island		57,648
Vermont		33,569
Delaware		49,760
District of Columbia		57,518
Maryland		3,80,172
New Jersey		6,02,297
New York		13,41,914
Pennsylvania		7,08,862
Illinois		7,25,394
Indiana		3,12,151
Michigan		4,75,626
Ohio		5,63,926
Wisconsin		2,95,073
Iowa		1,54,091
Kansas		1,46,028
Minnesota		3,16,327
Missouri		2,85,704
Nebraska.		1,00,534
North Dakota		41,277
South Dakota		44,236
Alabama		2,06,924
Arkansas		1,28,286
Florida		10,52,550
Georgia		4,81,213
Kentucky		1,86,685
Louisiana		2,12,223
Mississippi		1,13,469
North Carolina		4,75,927
South Carolina		2,17,276
Tennessee		3,19,401
Virginia		4,85,098
West Virginia		73,278
Arizona		3,13,040
New Mexico		86,328
Oklahoma		1,81,886
Texas		14,11,021
Colorado		3,23,767
Idaho		75,703
Montana		50,055
Utah		1,43,324
Wyoming		34,719
Alaska		44,015
California		24,75,727
Hawaii		77,509
Nevada		1,46,333
Oregon		2,09,148
Washington		4,58,017

The mean Personal Income [Millions of dollars] in all 50 states of United States for the year 2018 is 344567.2.

The Standard deviation of Personal Income [Millions of dollars] in all 50 states of the United States for the year 2018 is 432699.8.

80% Confidence Interval is calculated with the help of Excel and the output is below:

2,66,917.875	confidence interval 80.% lower
4,22,216.517	confidence interval 80.% upper
77,649.321	margin of error
60,590.087	std. error

Thus, 80% Confidence Interval is between 2,66,917.87 and 4,22,216.52 which states that there is 80% chance that the true mean of Personal Income is likely to be between 2,66,917.87 and 4,22,216.52.

Margin of Error for the Personal Income is 77,649.32 which asserts that the maximum amount by which the sample results are expected to differ from those of the actual value is 77,649.32.

95% Confidence Interval is calculated with the help of Excel and the output is as follows:

2,25,812.807	confidence interval 95.% lower
4,63,321.585	confidence interval 95.% upper
1,18,754.389	margin of error
60,590.087	std. error

Thus, 95% Confidence Interval is between 2,25,812.81 and 4,63,321.58 which states that there is 95% chance that the true mean of Personal Income is likely to be between 2,25,812.81 and 4,63,321.58.

Margin of Error for the Personal Income is 60,590.09 which asserts that the maximum amount by which the sample results are expected to differ from those of the actual value is 60,590.09.

99% Confidence Interval is calculated with the help of Excel and the output is below:

1,88,497.474	confidence interval 99.% lower
5,00,636.918	confidence interval 99.% upper
1,56,069.722	margin of error
60,590.087	std. error

Thus, 99% Confidence Interval is between 1,88,497.47 and 5,00,636.92 which states that there is a 99% chance that the true mean of Personal Income is likely to be between 1,88,497.47 and 5,00,636.92.

Margin of Error for the Personal Income is 1,56,069.72 which asserts that the maximum amount by which the sample results are expected to differ from those of the actual value is 1,56,069.72.

I would like to pick a Confidence Interval of 90% level.

90% Confidence Interval is calculated with the help of Excel and the output is below:

2,44,905.371	confidence interval 90.% lower
4,44,229.021	confidence interval 90.% upper
99,661.825	margin of error
60,590.087	std. error

Thus, a 90% Confidence Interval is between 2,44,905.37 and 4,44,229.02 which states that there is a 90% chance that the true mean of Personal Income is likely to be between 2,44,905.37 and 4,44,229.02.

Margin of Error for the Personal Income is 60,590.09 which asserts that the maximum amount by which the sample results are expected to differ from those of the actual value is 60,590.09.

The Confidence Intervals are as follows:

80% Confidence Interval is between 2,66,917.87 and 4,22,216.52.

90% Confidence Interval is between 2,44,905.37 and 4,44,229.02.

95% Confidence Interval is between 2,25,812.81 and 4,63,321.58.

99% Confidence Interval is between 1,88,497.47 and 5,00,636.92.

We can clearly observe that as the Confidence Interval is increasing, Lower limit is decreasing. Thus, we can conclude that there is an inverse relation between Confidence Interval and Lower limit.

We also see that as the Confidence Interval is increasing, Upper limit is increased. Thus, we can conclude that there is a direct relation between Confidence Interval and the Upper limit.

We also analyze that the range of the Confidence Interval is increasing as the Confidence Interval is increasing. This states that if the Confidence Interval is increased, then it is more likely to include the true mean of the Personal Income in it.

80% Confidence Interval is between 2,66,917.87 and 4,22,216.52 which states there is 80% chance that the true mean of Personal Income is likely to be between 2,66,917.87 and 4,22,216.52.

90% Confidence Interval is between 2,44,905.37 and 4,44,229.02 which states that there is a 90% chance that the true mean of Personal Income is likely to be between 2,44,905.37 and 4,44,229.02.

95% Confidence Interval is between 2,25,812.81 and 4,63,321.58 which states that there is a 95% chance that the true mean of Personal Income is likely to be between 2,25,812.81 and 4,63,321.58.

99% Confidence Interval is between 1,88,497.47 and 5,00,636.92 which states that there is a 99% chance that the true mean of Personal Income is likely to be between 1,88,497.47 and 5,00,636.92.

• Confidence Interval gives me an impression of the precision of the parameter estimate. Values spanned by this interval are seen as "not too unexpected to be true".
• Looking at mean values, giving the CI is not in principle different to giving the standard errors (both are measures of precision), but the CI is much easier and clearer to interpret than the standard errors since they directly give me a range of "not too unreasonable values" of the estimate.

Confidence Intervals are also used in day to day life and we don’t realize it because it’s not the formal CI. For instance, I may not know how much money is in my pocket down to the penny, but I do know if it's between $100 and $1. That's an estimation I can calculate with the help of CI.

But let's say that I want to maintain a certain range of cash, so at the end of every day I count all the cash I am carrying, and after several months I calculate the mean and standard deviation. Then I calculate out a CI. That's a pretty good indicator of how much money I am likely to carry on average from here forward, all other things being equal. The months of data collection can be seen as a sample of all the months to come, and even arguably months from the past too.

The same process can be undertaken with any kind of data in life: tire pressure, spending on video games (and video scores), rainfall, time to drive to work or school, prices of grocery items, volume of music heard from next door (in dB's), electric bills, prices of gasoline, time spent studying, amounts spent for lunches, times running the 100-meters, time spent with a BFF, and on and on.

Coming to my project, Confidence Interval can be used to make a good estimation of average Personal Income in all 50 States and the government can talk about the year budget accordingly. This can help in developing a wealthy economy.