A research organization has collected the following data on household size and telephone ownership for 200 U.S. households. At the 0.05 level, are the two variables independent? Based on the chi-square table, what is the most accurate statement that can be made about the p-value for the test?

Telephones Owned ¡Ü 1 2 ¡Ý 3 Total

Persons ¡Ü 2 49 18 13 80
In the 3-4 40 27 21 88
Household ¡Ý 5 11 13 8 32
100 58 42 200

3 answers

For three independent samples, each with n= 100, the respective sample proportions are 0.30, 0.35, and 0.25. Use the 0.05 level in testing whether the three population proportions could be the same.
For three independent samples, each with n= 100, the respective sample proportions are 0.30, 0.35, and 0.25. Use the 0.05 level in testing whether the three population proportions could be the same.
Here the number of degrees of freedom is (3-1)=2. Hence the continuity correction of 0.5 is not required.

The observations are 30,35 and 25, and the theoretical values are therefore (30+35+25)/3=30
Χ²
=(30-30)²/30+(35-30)²/30+(25-30)²/30
=0+0.833+0.833
=1.667
At α=0.05, . prob.=0.95 and DF=2, Χ²=5.99
Since Χ²=1.667<5.99, we conclude that the hypothesis that the three populations are the same is not rejected.
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