Question

In: Statistics and Probability

The following table provides information on life expectancies for a sample of 22 countries. It also...

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.

Solutions

Expert Solution

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


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