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?

Question

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

Answer 1

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.

Answer 2

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.

Answer 3

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.