# Descriptive Statistics Interpreting Data Sets

The data on the left is the level of GDP freedom for 42 nations

1. Run descriptive statistics on this data set and interpret the meaning (this does not mean just repeating the numbers)

2. Create a 90%, 95%, and 99% confidence interval and explain what this means

3. Do a hypothesis test and check to see if a value of a single value of 5.0E+11* is realistic based on the data and state why, you must show all the steps in the hypothesis test

4. Do a hypothesis test and check to see if a value of a sample with 30 observations that has a value of 5.0E+11 is realistic based on the data you must show all the steps in the hypothesis test

*5.0E+11 = 500,000,000,000 - It means add 11 zeros to the value - You do not need to change data, Excel will recognize and do as is

GDP

17243112604

84390572977

11786099138

1.94122E+12

2.97648E+11

3.68736E+11

9371187176

1211324626

3.79069E+11

51774221669

1610544922

4.69374E+11

6633055846

8820312674

1.00357E+11

47714490183

7538000000

16577887610

54713128376

1401000000

19649724656

2.08789E+12

4109500000

1516078205

14857275330

2013014939

1.57704E+12

5.2792E+11

2.12741E+11

5.92661E+12

22780280530

22393529278

11897620542

2.88189E+11

541097513

1648089240

35831464226

23132450331

1.92032E+11

3.28053E+12

466389674.1

3.09866E+11

https://brainmass.com/statistics/confidence-interval/descriptive-statistics-interpreting-data-sets-485350

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please see the attachment.

The data on the left is the level of GDP freedom for 42 nations

1. Run descriptive statistics on this data set and interpret the meaning (this does not mean just repeating the numbers).

Descriptive statistics

GDP

count 42

mean 439,067,701,244.41

sample variance 1,208,846,132,167,010,000,000,000.00

sample standard deviation 1,099,475,389,523.12

minimum 466389674.1

maximum 5.92661E+12

range 5.92614E+12

1st quartile 7,858,578,168.50

median 22,956,365,430.50

3rd quartile 295,283,250,000.00

interquartile range 287,424,671,831.50

The average GDP is 439,067,701,244.41 with a standard deviation of 1,099,475,389,523.12. The box plot and histogram suggest that the distribution of GDP is highly positively skewed and there are some extreme values in the data.

2. Create a 90%, 95%, and 99% confidence interval and explain what this means.

Confidence interval for population mean is given by the formula

Details

90% Confidence interval

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation 1.09948E+12

Sample Mean 439067701244

Sample Size 42

Confidence Level 90%

Intermediate Calculations

Standard Error of the Mean 1.69653E+11

Degrees of Freedom 41

t Value 1.6829

Interval Half Width 285504857166.8830

Confidence Interval

Interval Lower Limit 153562844077.52

Interval Upper Limit 724572558411.29

With 90% confidence we can claim that the population mean GDP is within the limits (153562844077.52, 724572558411.29)

95% Confidence interval

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation 1.09948E+12

Sample Mean 439067701244

Sample Size 42

Confidence Level 95%

Intermediate Calculations

Standard Error of the Mean 1.69653E+11

Degrees of Freedom 41

t Value 2.0195

Interval Half Width 342620646941.8150

Confidence Interval

Interval Lower Limit 96447054302.59

Interval Upper Limit 781688348186.22

With 95% confidence we can claim that the population mean GDP is within the limits (96447054302.59, 781688348186.22)

99% Confidence interval

Confidence Interval Estimate for the Mean

Data

Sample Standard Deviation 1.09948E+12

Sample Mean 439067701244

Sample Size 42

Confidence Level 99%

Intermediate Calculations

Standard Error of the Mean 1.69653E+11

Degrees of Freedom 41

t Value 2.7012

Interval Half Width 458262797110.4050

Confidence Interval

Interval Lower Limit -19195095866.00

Interval Upper Limit 897330498354.81

With 99% confidence we can claim that the population mean GDP is within the limits (-19195095866.00, 897330498354.81)

3. Do a hypothesis test and check to see if a value of a single value of 5.0E+11* is realistic based on the data and state why, you must show all the steps in the hypothesis test.

H0: Population mean GDP = 5.0E11

H1: Population mean GDP ≠ 5.0E11

Test Statistic used is one sample t test.

Significance level = 0.05

Decision rule : Reject the null hypothesis if the value of test statistic is greater than the critical value.

Details

t Test for Hypothesis of the Mean

Data

Null Hypothesis = 5.00E+11

Level of Significance 0.05

Sample Size 42

Sample Mean 439067701244

Sample Standard Deviation 1.09948E+12

Intermediate Calculations

Standard Error of the Mean 169652735804.2930

Degrees of Freedom 41

t Test Statistic -0.3592

Two-Tail Test

Lower Critical Value -2.0195

Upper Critical Value 2.0195

p-Value 0.7213

Do not reject the null hypothesis

Conclusion: Fails to reject the null hypothesis. The sample provides enough evidence to support the claim that Population mean GDP = 5.0E+11.

4. Do a hypothesis test and check to see if a value of a sample with 30 observations that has a value of 5.0E+11 is realistic based on the data you must show all the steps in the hypothesis test.

H0: Population mean GDP = 5.0E11

H1: Population mean GDP ≠ 5.0E11

Test Statistic used is one sample t test.

Significance level = 0.05

Decision rule : Reject the null hypothesis if the value of test statistic is greater than the critical value.

Details

t Test for Hypothesis of the Mean

Data

Null Hypothesis = 5.00E+11

Level of Significance 0.05

Sample Size 30

Sample Mean 431365028396

Sample Standard Deviation 1.15511E+12

Intermediate Calculations

Standard Error of the Mean 210892926683.5510

Degrees of Freedom 29

t Test Statistic -0.3254

Two-Tail Test

Lower Critical Value -2.0452

Upper Critical Value 2.0452

p-Value 0.7472

Do not reject the null hypothesis

Conclusion: Fails to reject the null hypothesis. The sample provides enough evidence to support the claim that Population mean GDP = 5.0E+11.

https://brainmass.com/statistics/confidence-interval/descriptive-statistics-interpreting-data-sets-485350