DISPLAYING AND DESCRIBING DISTRIBUTIONS In this lab assignment you will use expl

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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

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

Explanation / Answer

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:

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

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