In: Statistics and Probability
DISPLAYING AND DESCRIBING DISTRIBUTIONS
In this lab assignment you will use exploratory tools in StatCrunch to study the wealth and life expectancy in 97 countries. In particular, you will learn how to display the related categorical and quantitative data with pie charts, histograms, and boxplots, and how to summarize the data by obtaining contingency table, mean, median, standard deviation, and quartiles. You will also explore the relationship between material wealth and life expectancy with a scatter-plot.
Wealth and Life Expectancy
In recent years an impressive body of evidence has emerged that shows how population health is influenced by social and economic conditions. In particular, there is strong evidence of a relationship between longevity measured by life expectancy and material wealth measured by Gross National Product (GNP).
The assignment is based on data collected from the U.N.E.S.C.O. 1990 Demographic Year Book and The Annual Register 1992 that provides birth rates, death rates, life expectancies for males and females, and Gross National Products for 97 countries. You will use the data to examine the wealth and life expectancies of six different country groups and their population growth.
The data are available in the StatCrunch file lab1.txt located on STAT 151 Laboratories web site at http://www.stat.ualberta.ca/statslabs/stat151/index.htm (click Stat 151 link, and Data for Lab 1). The missing data are marked with asterisks. The following is a description of the variables in the data file:
Variable Name Description of Variable
COUNTRY Country
BIRTH Live birth rate per 1,000 of population,
DEATH Death rate per 1,000 of population ,
LEXPM Life expectancy at birth for males,
LEXPF Life expectancy at birth for females,
GNP Gross National Product (GNP) per capita,
GROUP 1= Eastern Europe; 2= South America and Mexico; 3= Western Europe, North America, Japan, Australia, New Zealand; 4= Middle East; 5= Asia; 6= Africa.
here is the data
COUNTRY BIRTH DEATH LEXPM LEXPF GNP GROUP Albania 24.7 5.7 69.6 75.5 600 1 Bulgaria 12.5 11.9 68.3 74.7 2250 1 Czechoslovakia 13.4 11.7 71.8 77.7 2980 1 Former_E._Germany 12 12.4 69.8 75.9 * 1 Hungary 11.6 13.4 65.4 73.8 2780 1 Poland 14.3 10.2 67.2 75.7 1690 1 Romania 13.6 10.7 66.5 72.4 1640 1 Yugoslavia 14 9 68.6 74.5 * 1 USSR 17.7 10 64.6 74 2242 1 Byelorussian_SSR 15.2 9.5 66.4 75.9 1880 1 Ukrainian_SSR 13.4 11.6 66.4 74.8 1320 1 Argentina 20.7 8.4 65.5 72.7 2370 2 Bolivia 46.6 18 51 55.4 630 2 Brazil 28.6 7.9 62.3 67.6 2680 2 Chile 23.4 5.8 68.1 75.1 1940 2 Columbia 27.4 6.1 63.4 69.2 1260 2 Ecuador 32.9 7.4 63.4 67.6 980 2 Guyana 28.3 7.3 60.4 66.1 330 2 Paraguay 34.8 6.6 64.4 68.5 1110 2 Peru 32.9 8.3 56.8 66.5 1160 2 Uruguay 18 9.6 68.4 74.9 2560 2 Venezuela 27.5 4.4 66.7 72.8 2560 2 Mexico 29 23.2 62.1 66 2490 2 Belgium 12 10.6 70 76.8 15540 3 Finland 13.2 10.1 70.7 78.7 26040 3 Denmark 12.4 11.9 71.8 77.7 22080 3 France 13.6 9.4 72.3 80.5 19490 3 Germany 11.4 11.2 71.8 78.4 22320 3 Greece 10.1 9.2 65.4 74 5990 3 Ireland 15.1 9.1 71 76.7 9550 3 Italy 9.7 9.1 72 78.6 16830 3 Netherlands 13.2 8.6 73.3 79.9 17320 3 Norway 14.3 10.7 67.2 75.7 23120 3 Portugal 11.9 9.5 66.5 72.4 7600 3 Spain 10.7 8.2 72.5 78.6 11020 3 Sweden 14.5 11.1 74.2 80 23660 3 Switzerland 12.5 9.5 73.9 80 34064 3 U.K. 13.6 11.5 72.2 77.9 16100 3 Austria 14.9 7.4 73.3 79.6 17000 3 Japan 9.9 6.7 75.9 81.8 25430 3 Canada 14.5 7.3 73 79.8 20470 3 U.S.A. 16.7 8.1 71.5 78.3 21790 3 Bahrain 28.4 3.8 66.8 69.4 6340 4 Iran 42.5 11.5 55.8 55 2490 4 Iraq 42.6 7.8 63 64.8 3020 4 Israel 22.3 6.3 73.9 77.4 10920 4 Jordan 38.9 6.4 64.2 67.8 1240 4 Kuwait 26.8 2.2 71.2 75.4 16150 4 Lebanon 31.7 8.7 63.1 67 * 4 Oman 45.6 7.8 62.2 65.8 5220 4 Saudi_Arabia 42.1 7.6 61.7 65.2 7050 4 Turkey 29.2 8.4 62.5 65.8 1630 4 United_Arab_Emirates 22.8 3.8 68.6 72.9 19860 4 Afghanistan 40.4 18.7 41 42 168 5 Bangladesh 42.2 15.5 56.9 56 210 5 Cambodia 41.4 16.6 47 49.9 * 5 China 21.2 6.7 68 70.9 380 5 Hong_Kong 11.7 4.9 74.3 80.1 14210 5 India 30.5 10.2 52.5 52.1 350 5 Indonesia 28.6 9.4 58.5 62 570 5 Korea 23.5 18.1 66.2 72.7 * 5 Malaysia 31.6 5.6 67.5 71.6 2320 5 Mongolia 36.1 8.8 60 62.5 110 5 Nepal 39.6 14.8 50.9 48.1 170 5 Pakistan 30.3 8.1 59 59.2 380 5 Philippines 33.2 7.7 62.5 66.1 730 5 Singapore 17.8 5.2 68.7 74 11160 5 Sri_Lanka 21.3 6.2 67.8 71.7 470 5 Thailand 22.3 7.7 63.8 68.9 1420 5 Vietnam 31.8 9.5 63.7 67.9 * 5 Algeria 35.5 8.3 61.6 63.3 2060 6 Angola 47.2 20.2 42.9 46.1 610 6 Botswana 48.5 11.6 52.3 59.7 2040 6 Congo 46.1 14.6 50.1 55.3 1010 6 Egypt 38.8 9.5 57.8 60.3 600 6 Ethiopia 48.6 20.7 42.4 45.6 120 6 Gabon 39.4 16.8 49.9 53.2 390 6 Gambia 47.4 21.4 41.4 44.6 260 6 Ghana 44.4 13.1 52.2 55.8 390 6 Kenya 47 11.3 56.5 60.5 370 6 Libya 44 9.4 59.1 62.56 5310 6 Malawi 48.3 25 38.1 41.2 200 6 Morocco 35.5 9.8 59.1 62.5 960 6 Mozambique 45 18.5 44.9 48.1 80 6 Namibia 44 12.1 55 57.5 1030 6 Nigeria 48.5 15.6 48.8 52.2 360 6 Sierra_Leone 48.2 23.4 39.4 42.6 240 6 Somalia 50.1 20.2 43.4 46.6 120 6 South_Africa 32.1 9.9 57.5 63.5 2530 6 Sudan 44.6 15.8 48.6 51 480 6 Swaziland 46.8 12.5 42.9 49.5 810 6 Tunisia 31.1 7.3 64.9 66.4 1440 6 Uganda 52.2 15.6 49.9 52.7 220 6 Tanzania 50.5 14 51.3 54.7 110 6 Zaire 45.6 14.2 50.3 53.7 220 6 Zambia 51.1 13.7 50.4 52.5 420 6 Zimbabwe 41.7 10.3 56.5 60.1 640 6
5. Now you will compare the distributions of life expectancy among the 6 groups separately for each gender.
(d) Obtain a new variable LEXPF-LEXPM which is the difference between female and male life expectancy for each country. Obtain the summary statistics for the new variable for each group. Paste the output into your report. Do females tend to live longer, on average, than males? From all countries, what are the minimum and maximum differences? In which countries do these occur?
I'm just unsure what this question is really asking for... thanks
First find the mean and variance of each group life expectancy.
in part (d), make one column of LEXPF-LEXPM, in this column subtract
LEXPM (Life expectancy at birth for males) and LEXPF (Life expectancy at birth for females).
For example:
COUNTRY BIRTH DEATH LEXPM LEXPF GNP GROUP LEXPF - LEXPM Albania 24.7 5.7 69.6 75.5 600 1 5.9 Bulgaria 12.5 11.9 68.3 74.7 2250 1 6.4 Czechoslovakia 13.4 11.7 71.8 77.7 2980 1 5.9
Former_E._Germany 12 12.4 69.8 75.9 * 1 6.1 Hungary 11.6 13.4 65.4 73.8 2780 1 8.4 Poland 14.3 10.2 67.2 75.7 1690 1 8.5 Romania 13.6 10.7 66.5 72.4 1640 1 5.9 Yugoslavia 14 9 68.6 74.5 * 1 5.9 USSR 17.7 10 64.6 74 2242 1 9.4 Byelorussian_SSR 15.2 9.5 66.4 75.9 1880 1 9.5 Ukrainian_SSR 13.4 11.6 66.4 74.8 1320 1 8.4 Argentina 20.7 8.4 65.5 72.7 2370 2 7.2 Bolivia 46.6 18 51 55.4 630 2 4.4 Brazil 28.6 7.9 62.3 67.6 2680 2 5.3 Chile 23.4 5.8 68.1 75.1 1940 2 7.0 Columbia 27.4 6.1 63.4 69.2 1260 2 5.8 Ecuador 32.9 7.4 63.4 67.6 980 2 4.2 Guyana 28.3 7.3 60.4 66.1 330 2 5.7 Paraguay 34.8 6.6 64.4 68.5 1110 2 4.1 Peru 32.9 8.3 56.8 66.5 1160 2 9.7 Uruguay 18 9.6 68.4 74.9 2560 2 6.5 Venezuela 27.5 4.4 66.7 72.8 2560 2 6.1 Mexico 29 23.2 62.1 66 2490 2 3.9
Similarly find for other groups.
Mean of LEXPF-LEXPM = (Sum of all values in column LEXPF-LEXPM in a group) / (number of countries in that group)
For group 1: there are 11 countries.
Mean of LEXPF-LEXPM of group 1 = 7.3
Similarly find mean for other groups
Find Second Moments of each group
Second moments = (Sum of square of all entries of LEXPF-LEXPM column in a group) / (total number of countries in that group)
Find variance of each country
Variance of each country = (Second moment of that country's LEXPF-LEXPM) - (mean of that country's LEXPF-LEXPM)^(2).
Now you have the statistics for each group.
Do females tend to live longer, on average, than males?
For this perform hypothesis testing
Null Hypothesis: LEXPF-LEXPM =0
Alternate Hypothesis: LEXPF-LEXPM > 0