In: Statistics and Probability
The following table provides information on life expectancies for a sample of 22 countries. It also lists the number of people per television set in each country.
Country |
Life Expectancy |
People Per TV |
Angola |
44 |
200 |
Australia |
76.5 |
2 |
Cambodia |
49.5 |
177 |
Canada |
76.5 |
1.7 |
China |
70 |
8 |
Egypt |
60.5 |
15 |
France |
78 |
2.6 |
Haiti |
53.5 |
234 |
Iraq |
67 |
18 |
Japan |
79 |
1.8 |
Madagascar |
52.5 |
92 |
Mexico |
72 |
6.6 |
Morocco |
64.5 |
21 |
Pakistan |
56.5 |
73 |
Russia |
69 |
3.2 |
South Africa |
64 |
11 |
Sri Lanka |
71.5 |
28 |
Uganda |
51 |
191 |
United Kingdom |
76 |
3 |
United States |
75.5 |
1.3 |
Vietnam |
65 |
29 |
Yemen |
50 |
38 |
Instructions: When Minitab is used to answer a question below, copy the output from Minitab into your document.
Use Minitab to produce a scatterplot of life expectancy vs. people per television set. Does there appear to be an association between the two variables? Elaborate briefly.
Have Minitab calculate the value of the Pearson correlation coefficient between life expectancy and people per television.
Since the association is so strongly negative, one might conclude that simply sending television sets to the countries with lower life expectancies would cause their inhabitants to live longer. Comment on this argument.
If two variables have a correlation close to +1 or –1, indicating a strong linear association between them, does it follow that there must be a cause-and-effect relationship between them?
This example illustrates the very important distinction between association and causation. Two variables may be strongly associated (as measured by the correlation coefficient) without a cause-and-effect relationship existing between them. Often the explanation is that both variables are related to a third variable not being measured; this variable is often called a lurking variable.
In the case of life expectancy and television sets, suggest a lurking variable that is associated both with a country’s life expectancy and with the prevalence of televisions in the country.
Sol:
select the data
go to
Graph>Scatterplot>select Y as people per TV
X as life expectancy
click ok
we get
From scatterplot we observe there is a negative correlation between life expectancy and people per TV
To get the pearson coorelation oin minitab.Go to
Stat>Basic statistics>correlation
selct the varibales
click pearson
we get
Output:
Correlation: Life expectancy, people per TV
Pearson correlation of Life expectancy and people per TV =
-0.798
P-Value = 0.000
r=-0.798
p=0.000
p<0.05
There is strong negative relationship between Life expectancy, people per TV and it is statistically significant
If two variables have a correlation close to +1 or –1, indicating a strong linear association between them, does it follow that there must be a cause-and-effect relationship between them?
correlation does not imply causation.
NO
Since the association is so strongly negative, one might conclude that simply sending television sets to the countries with lower life expectancies would cause their inhabitants to live longer
we can say only association between variables,we cannot establish cause and effect relationship with correlation
NO