MATH 399N Statistics

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Running head: GUIDED IMAGERY AND PROGRESSIVE MUSCLE RELAXATION

2

12

Course Project Part I

Chamberlain University College of Nursing

MATH399 Applied Managerial Statistics

December 5, 2020

Course Project Part I

Introduction

The topic under analysis is the personal income in different states in 2018. The focus of the analysis is to determine the states where personal incomes are reducing and where it is increasing to establish its effect on the economy. The incomes earned by residents in the 50 states and the District of Columbia come from dividends, government benefits, wages, rents, proprietors’ incomes, and interest. The data is obtained from the Bureau of Economic Analysis, which is a website by the United States government.

https://www.bea.gov/news/2020/real-personal-income-state-and-metropolitan-area-2018

Sample Data—

 

Personal income [Millions of dollars]

2017

2018

Percent change

United States1

16,870,106

17,813,035

5.6

Alabama

197,283

206,455

4.6

Alaska

42,015

43,818

4.3

Arizona

299,613

317,913

6.1

Arkansas

124,684

130,297

4.5

California

2,370,112

2,514,129

6.1

Colorado

310,755

332,943

7.1

Connecticut

258,079

273,152

5.8

Delaware

48,189

50,783

5.4

District of Columbia

54,938

57,605

4.9

Florida

1,004,144

1,066,447

6.2

Georgia

463,756

488,964

5.4

Hawaii

75,689

78,721

4.0

Idaho

72,355

77,012

6.4

Illinois

689,724

724,189

5.0

Indiana

301,203

315,516

4.8

Iowa

149,191

158,197

6.0

Kansas

142,242

149,859

5.4

Kentucky

182,605

189,717

3.9

Louisiana

205,227

215,489

5.0

Maine

62,173

65,454

5.3

Maryland

364,576

382,829

5.0

Massachusetts

468,300

494,765

5.7

Michigan

461,486

484,030

4.9

Minnesota

305,795

322,728

5.5

Mississippi

108,749

112,992

3.9

Missouri

279,433

292,513

4.7

Montana

47,718

50,500

5.8

Nebraska

97,151

102,759

5.8

Nevada

139,449

149,219

7.0

New Hampshire

78,822

83,143

5.5

New Jersey

577,081

607,884

5.3

New Mexico

82,733

87,189

5.4

New York

1,286,023

1,341,932

4.3

North Carolina

453,769

478,862

5.5

North Dakota

39,775

42,148

6.0

Ohio

544,141

569,727

4.7

Oklahoma

171,597

182,302

6.2

Oregon

200,579

213,070

6.2

Pennsylvania

679,731

720,073

5.9

Rhode Island

55,337

57,994

4.8

South Carolina

211,299

222,189

5.2

South Dakota

43,275

46,066

6.5

Tennessee

301,560

317,515

5.3

Texas

1,357,466

1,445,270

6.5

Utah

136,544

146,423

7.2

Vermont

32,461

33,929

4.5

Virginia

468,177

492,313

5.2

Washington

434,759

467,399

7.5

West Virginia

70,218

73,809

5.1

Wisconsin

285,487

299,933

5.1

Wyoming

32,639

34,873

6.8

1. Problem Computations:

· Determine the mean and standard deviation of your sample.

The mean of the personal income in all 50states is 344567.2 (millions of dollars)

The standard deviation of the incomes is 432699.8 (millions of dollars)

· Find the 80%, 95%, and 99% confidence intervals.

The 80% confidence interval is;

The margin of error for the state’s personal income is 77,649.32, which means that the expected results from the sample will differ from the actual income value by 77,649.32.

The 95% confidence interval is below;

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

The margin of error for personal income is 60,590.09, which means that the expected results from the sample will differ from the actual income value by 60,590.09.

For the 99% confidence interval;

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

The margin of error is 1,56,069.72, which is the most amount by which the results of the sample will vary from the actual value by 1,56,069.72.

· My confidence interval

My confidence interval is at the 90% level as calculated 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

The margin of error is 60,590.09, which is the most amount that would vary from the actual value of 60,590.08.

Problem Analysis

As the confidence interval increases, the lower limit is declining. This suggests an inverse relationship between the lower limit and the confidence level. As the confidence level rises, the upper limit also goes up. This suggests that there is a direct link between the upper limit and the confidence interval.

In this case, the 80% confidence interval is located between 2,66,917.88 and 4,22,216.52. This also means that there is an 80% chance that the actual personal income mean is between the two values above. The confidence interval is located between 2,25,812.80 and 4,63,321.59, which also means that this would be the true mean personal income has a 95% chance to be between the two values. The confidence interval is between 2,44,905.371 and 4,44,229.021 that suggests the true personal income has a 90% chance that it would be between the two values. The 99% confidence interval is between 5,00,636.92 and 1,88,497.47, and this means that there is a 99% chance that the personal income is also between the two variables.

Part I of the project has helped me understand the accuracy of the estimate provided and that the values based on the intervals seem unexpected. The confidence interval is also clearer and easier to interpret when compared to standard errors, which give a range of values that are almost accurate. The project has allowed me to understand how to use the confidence interval to get the average personal income in 50 states. The data can help make plans to develop the economy.

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