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In: Statistics and Probability

DISPLAYING AND DESCRIBING DISTRIBUTIONS In this lab assignment you will use exploratory tools in StatCrunch to...

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

Solutions

Expert Solution

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

orchestra answered 2 years ago
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