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# Descriptive Statistics Interpreting Data Sets

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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!

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.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!