# ANOVA, Chi-square tests

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Question # 3. Refer to the OECD data, which reports information on census, economic, and business data for 29 countries:

a) Categorize the 29 countries, indicating whether they are in Europe, North America, or the Far East. At the .05 significance level, is there a difference in the mean percent of the population over 65 years of age?

b) Use the same categories developed in part (a). Divide the gross national product by the population to create a new variable. This variable shows the per capita GNP. At the .05 significance level, is there a difference in the mean of this variable by geographic region?

OECD Data

X1 = Country

X2 = G7 member (1 - Yes, 0 = No)

X3 = Total Area of country in thousand square kilometers

X4 = Population in thousands

X5 = Percent of population over 65 years of age

X6 = Exchange rate per U S dollar

X7 = Gross domestic product at current exchange rate in billions of dollars

X8 = Energy use in millions of tons of oil equivalent

X9 = Index of total manufacturing (1900 = 100)

X10 = Total labor force in thousands

X11 = Region (1 = Far East, 2 = Europe, 3 = North America)

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11

Australia 0 7,687 18,289 12.1 1.509 390.9 100.61 109 9184 1

Austria 0 84 8,060 15 12.51 228.7 27.19 111 3876 2

Belgium 0 31 10,157 16.1 36.61 268.2 56.4 108 4297 2

Canada 1 9,976 29,964 12.2 1.426 579.2 236.17 112 15209 3

Czech Rep 0 79 10,316 13.4 34.73 56.2 40.4 5175 2

Denmark 0 43 5,262 15.1 6.771 174.9 22.87 117 2822 2

Finland 0 338 5,125 14.4 5.369 125.1 31.48 121 2531 2

France 1 549 58,380 15.3 5.955 1536.6 254.2 98 25613 2

Germany 1 357 81,877 15.8 1.777 235.35 349.55 97 39294 2

Greece 0 132 10,465 15.8 279.6 122.4 24.39 98 4249 2

Hungary 0 93 10,193 14.2 201.3 44 25.47 4048 2

Iceland 0 103 270 11.4 71.71 7.3 2.27 148 2

Ireland 0 70 3,621 11.5 0.687 70.7 11.96 175 1494 2

Italy 1 301 57,473 15.8 1743 1243.2 161.14 104 23385 2

Japan 1 378 125,864 14.5 129.4 4595.2 510.36 98 67110 1

Korea 0 98 45,545 6.1 1477 484.8 162.87 163 21188 1

Luxembourg 0 3 418 14.2 17 3.45 100 218 2

Mexico 0 1,973 96,582 4.8 8.123 329.4 141.38 118 34325 3

Netherlands 0 41 15,494 13.3 2.004 396 75.8 109 7516 2

New Zealand 0 269 3,640 11.6 1.689 65.9 16.3 119 1797 1

Norway 0 324 4,370 15.9 7.25 157.8 23.15 115 2246 2

Poland 0 313 38,618 11.3 3.532 134.4 108.41 17203 2

Portugal 0 92 9,935 14.8 181.5 103.6 19.15 97 4885 2

Spain 0 505 39,270 15.6 150.3 584.9 101.41 103 16159 2

Sweden 0 450 8,901 17.3 7.785 251.7 52.57 121 4310 2

Switzerland 0 41 7,085 14.9 1.44 294.3 25.62 103 3967 2

Turkey 0 781 62,695 4.8 199,026 181.5 65.52 129 22736 2

United King 1 245 58,782 15.7 0.603 1153.4 234.72 102 28552 2

United States 1 9,373 265,557 12.8 1 7388. 2134.96 118 135231 3

Question # 4: The manufacturer of a computer terminal reports in its advertising that the mean life of the terminal, under normal use, is 6 years, with a standard deviation of 1.4 years. (Assume this are population values) A sample of 90 units sold 10 years ago revealed the following distribution of the lengths of life. At the, 05 significance level, can the manufacturer conclude that the terminal lives are normally distributed?

Length of life

(years) Frequency

Up to 4 7

4 up to 5 14

5 up to 6 25

6 up to 7 22

7 up to 8 16

8 or more 6

Question # 5

Two hundred managers from various levels were randomly selected and interviewed regarding their concern about environmental issues. The response of each person was tallied into one of three categories: no concern, same concern, and great concern. The results were:

Level of management No concern some concern great concern

Top management 15 13 12

Middle management 20 19 21

Supervisor 7 7 6

Group leader 28 21 31

Use the .01 significance level to determine whether there is a relationship between management level and environmental concern.

Please see the attached file for a detailed description of the questions.

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##### Solution Summary

The solution tests hypotheses- ANOVA for test of difference between means, Chi square test for goodness of fit, Chi square test for independence of variables.

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