Calculate the 90%, 95%, and 99% confidence intervals. Interpret the results from

Question

Calculate the 90%, 95%, and 99% confidence intervals. Interpret the results from your calculations.

My calculations are as follows:

Health Care Administrators salaries based on years of experience

State

Entry level

Mid level

Experienced

Hawaii

$77,580

$111,460

$127,770

Alabama

$62,734

$84,919

$96,013

Delaware

$81,474

$112,528

$128,419

Florida

$77,958

$103,480

$145,350

Kentucky

$54,564

$100,679

$162,907

Massachusetts

$69,853

$91,832

$134,304

Mississippi

$58,200

$94,920

$98,280

New York

$76,020

$123,620

$147,430

North Carolina

$69,500

$106,160

$124,500

Philadelphia Pennsylvania

$68,090

$111,290

$132,890

Mean

69,597.30

$1,040,888

1,297,863

Median

69,676.50

104,820

130,654.50

Mode

None

None

None

Standard Deviation

8492.833

10848.7062

19615.593

Health Care Administrators salaries based on years of experience

State

Entry level

Mid level

Experienced

Hawaii

$77,580

$111,460

$127,770

Alabama

$62,734

$84,919

$96,013

Delaware

$81,474

$112,528

$128,419

Florida

$77,958

$103,480

$145,350

Kentucky

$54,564

$100,679

$162,907

Massachusetts

$69,853

$91,832

$134,304

Mississippi

$58,200

$94,920

$98,280

New York

$76,020

$123,620

$147,430

North Carolina

$69,500

$106,160

$124,500

Philadelphia Pennsylvania

$68,090

$111,290

$132,890

Mean

69,597.30

$1,040,888

1,297,863

Median

69,676.50

104,820

130,654.50

Mode

None

None

None

Standard Deviation

8492.833

10848.7062

19615.593

Explanation / Answer

Find the mean and standard deviation for each of the column (the standard deviation given is wrong, divide it by n-1 instead of n because it is sample standard deviation)

confidence intervals = mean +/- standard deviation * zscore (for that confidence level)

z score for 95% confidence level can be looked up in the normal tables for value 0.975. But 0.975 because 0.025 on either side of the curve gives 95% percentile. It will give a z-score of 1.96

similarly for 90% confidence level, z-score is 1.64

similarly for 99% confidence level, z-score is 2.58

State Entry level Mid level Experienced Hawaii            77,580          111,460          127,770 Alabama            62,734            84,919            96,013 Delaware            81,474          112,528          128,419 Florida            77,958          103,480          145,350 Kentucky            54,564          100,679          162,907 Massachusetts            69,853            91,832          134,304 Mississippi            58,200            94,920            98,280 New York            76,020          123,620          147,430 North Carolina            69,500          106,160          124,500 Philadelphia Pennsylvania            68,090          111,290          132,890 mean            69,597          104,089          129,786 standard deviation              8,952            11,436            20,677 ci levl 95% 95% 95% z score                 1.96                 1.96                 1.96 upper ci = mean +zscore*SD            87,143          126,502          170,312 lower ci = mean -zscore*SD            52,051            81,676            89,261 ci levl 90% 90% 90% z value                 1.64                 1.64                 1.64 upper ci            84,322          122,899          163,796 lower ci            54,872            85,279            95,776 ci levl 99% 99% 99% z value                 2.58                 2.58                 2.58 upper ci            92,657          133,545          183,046 lower ci            46,538            74,633            76,527

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