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Difference

1725

14-1020

4035302822155

 A What sample size should she select?

Population Standard Deviation 30

Sampling Error 5Confidence Level 95%

Z Value -1.95996398Calculated Sample Size 138.292518

Sample Size Needed 139

3.8416 900

25

138.2976

B Construct a 90% confidence interval estimate for the population proportion of reimbursetments th

Sample Size 139Number of Successes 12Confidence Level 90%

Sample Proportion 0.08633094Z Value -1.64485363

INTERMEDIATE CALCULATION

DATA

INTERMEDIATE CALCULATION

RESULT

DATA

139

2976.138

5

3096.12

22

2

22

2/

n

n

n

e

 Z n a   

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Standard Error of the Proportion 0.02382156Interval Half Width 0.03918299

Interval Lower Limit 0.04714795Interval Upper Limit 0.12551392

0.0863

0.0863139

0.0006

0.0238

0.0392

0.04710.1255

C Construct a 95% confidence interval estimate for the population mean reimbursetments per office

Sample Standard Deviation 13.527Sample Mean 20.083Sample Size 139Confidence Level 95%

Standard Error of the Mean 1.147Degrees of Freedom 138

t α/2 Value 1.977

Interval Half Width 2.269

Interval Lower Limit 17.815Interval Upper Limit 22.352

from table above shows that:sample mean = 20.083sample standard deviation = 13.527for 95% confidence, cumulative probability = 0.975

since we have 139 sample size so that we get 138 degrees of freedom, from table E.3 we interpol

Degrees of Freedom

110

CONFIDENCE INTERVAL

DATA

INTERMEDIATE CALCULATIONS

CONFIDENCE INTERVAL

Cumulative Probabilities = 0.975

1.9818

1255.00471.0

0392.00863.0

0238.0645.10863.0139

0863.010863.0645.10863.0

12/

 

 

n

 p p Z  p

0863.0139

12

n

 X  p

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120138 ← results of 

-0.0019

-0.0053

1.9765

2.268 17.81622.351

D Construct a 95% confidence interval estimate for the population total amount of reimbursetments f 

Population Size 25,056Sample Mean 93.70$

Sample Size 139Sample Standard Deviation 34.55$Confidence Level 95%

Population Total 2,347,747FPC Factor 0.99724226Standard Error of the Total 73,224

Degrees of Freedom 138t  Value 1.9773Interval Half Width 144785.946

Interval Lower Limit 2,202,961$Interval Upper Limit 2,492,533$

1.97651.9799

DATA

INTERMEDIATE CALCULATIONS

CONFIDENCE INTERVAL

351.22816.17

268.2083.20

139

527.13)9765.1(083.20

)2.8(2/

 

  equationn

S t  X 

9765.1

9818.10053.0

10

0019.0289818.1

0019.0289818.110

9818.10019.0

2810

9818.1

9818.19799.1

110138

110120

 X 

 X 

 X 

 X 

 X 

 X 

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E Construct a 95% confidence interval estimate for the total difference between the amount reimbur 

Population Size 25,056

Sample Size 139

Confidence Level 95%

Sum of Differences 241 Average Difference in Sample 1.73381295

Total Difference 43,442Standard Deviation of Differences 1.66327691FPC Factor 0.9972Standard Error of the Total Differen 3525.08483Degrees of Freedom 138t  Value 1.9773Interval Half Width 6970.16272

Interval Lower Limit 36,472Interval Upper Limit 50,413

Number of Differences Not = 0 12Number of Differences = 0 127SS for Differences Not = 0 0SS for Differences = 0 381.775633Sum of Squares 381.775633Variance of Differences 2.76649009

1.7338

17 233.056525 541.315514 150.4593

For standard deviation of differences:

DATA

INTERMEDIATE CALCULATIONS

CONFIDENCE INTERVAL

ADDITIONAL CALCULATIONS

3078.474,492,2$0922.020,203,2$

1078.727,1442.747,347,2

9972.09305.2184.523,492.747,347,2

1056,25

139056,25

139

55.349765.1056,2570.93056,25

12/

total  population

 N nt  N  X  N  

7338.1139

2411 n

 D D

n

i

i

2

D Dn

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-10 137.682420 333.653640 1464.3011

35 1106.639230 798.977328 689.9126

22 410.718315 175.9917

5 10.6680

1

1

nS  i D

6231.6 DS 

7139.185,714717.698,15

6211.743,270928.442,43

9972.05618.0184.523,490928.442,43

,25

0,25

139

6231.69765.1056,257338.1056,25

12/

differencetotal 

 N 

n N 

n

S t  N  D N  D 

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t contain errors.

CARA

CARA

ARA

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0.9137

visit.

te tα/2:

 

CARA

ARA

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interpolating

or this geographic are in June.

CARA

"MANUA

CARA

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2,347,747.2

49,523.1840

2.9305

0.9972

144,727.1078

2,203,020.09222,492,474.3078

edand the amount that the auditor determined should have been reimbursed.

6,053.375443.86506.6231

CARA

"MANUAL"

CARA

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43,442.0928

49,523.1840

0.5618

0.9972

27,743.6211

15,698.471771,185.7139

1056

13956

CARA

"MANUA

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