MS 150 Statistics Spring 2001 fx

Part I

Use this life expectancy to answer the following questions.

Location Life expectancy
at birth in years
American
Samoa
75.1
CNMI 75.5
Fiji 67.9
FSM 68.6
Guam 77.8
Kiribati 59.8
Marshall
Islands
65.5
Nauru 60.8
Palau 68.6
Samoa 69.2
Vanuatu 60.2
1. _________ Determine the sample size n.

2. _________ Calculate the sample mean .

3. _________ Determine the median.

4. _________ Determine the mode.

5. _________ Calculate the range.

6. _________ Calculate the sample standard deviation sx.

7. _________ Calculate the sample variance.

8. _________ Calculate the Coefficient of Variation.

9. Using the intervals specified in the bins column, fill in the frequency and relative frequency columns of the following table. The number in the bins column is the class upper limit.  Include the class upper limit in each interval.

Bins Frequency Relative
Frequency f/n
60 _________ _________
65 _________ _________
70 _________ _________
75 _________ _________
80 _________ _________
Sums: _________ _________
1. Draw a histogram of the Relative Frequency data using the following chart:

1. _________ What is the shape of the distribution?
2. _________ What is the probability that, for the Pacific Island locations above, the life expectancy will be greater than 60 but less than or equal to 65 years?

3. Construct a 95% confidence interval for the population mean m life expectancy for Pacific Islanders using the above data.  Presume for this example that the data distribution is sufficiently normal.  Note that n is less than 30. Use the sample mean and sample standard deviation to generate your maximal error of estimate.  Show all of your work either below or on the back of this sheet.

Degrees of freedom = __________

T-value = ____________

The maximal Error of Estimate E = _______________

The 95% confidence interval for m is  ____________ < m < ____________

4.   In the following exercise use your sample mean and sample standard deviation as population parameters.  That is, use your calculations in #2 above, the sample mean , for the population mean m.  Use your calculations in #6 above, the sample standard deviation sx, for the population standard deviation s.

Let the null hypothesis H0 be that the average life expectancy is m as calculated by you in question number two above.  Suppose in the year 2001 the actual average life expectancy for these same countries rises to 70 years.  At an alpha of 0.05, is this increase in the life expectancy statistically significantly higher than the present rate?

Do we reject H0 and say the rise is statistically significant or do we fail to reject H0 and say the change is random at a = 0.05?  Note that n is less than 30.   Show of your work where appropriate either here or on the back!

1. _______________ What is H0?

2. _______________ What is H1?

3. __________ What is a?

4. __________ What is the t-statistic?

5. __________ What is t-critical?

6. __________ Do we reject H0?

Part II

For this part use the following data:

Location Per Capita Income
in dollars
Life expectancy
at birth in years
American Samoa 3300 75.1
CNMI 13100 75.5
Fiji 2000 67.9
FSM 1900 68.6
Guam 20700 77.8
Kiribati 600 59.8
Marshall Islands 1500 65.5
Nauru 9400 60.8
Palau 6400 68.6
Samoa 1300 69.2
Vanuatu 1276 60.6
1. _________ Calculate the slope of the least squares line for the income and life expectancy data above.

2. What does of the sign of the slope tell us about this data?  That is, what type of correlation is this?

3. _________ Calculate the linear correlation coefficient r for the income and life expectancy columns.

4. _________ Is the correlation none, low, moderate, high, or perfect?

5. _________ Calculate the coefficient of determination.

6. What does the coefficient of determination tell us about the relationship between per capita income and life expectancy?

Life expectancy data is from:http://www.bartleby.com/151/a29.html
and http://www.cia.gov/cia/publications/factbook/geos/cq.html
Income data is from http://www.un.org/Depts/unsd/social/inc-eco.htm