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Chapter , Problem 6AYU(choose chapter or problem)
Problem 6AYU
The following table contains the number of successes and failures for three categories of a variable
|
Category 1 |
Category 2 |
Category 3 |
Success |
204 |
199 |
214 |
Failure |
96 |
121 |
98 |
Test whether the proportions are equal for each category at the α = 0.01 level of significance.
Questions & Answers
QUESTION:
Problem 6AYU
The following table contains the number of successes and failures for three categories of a variable
|
Category 1 |
Category 2 |
Category 3 |
Success |
204 |
199 |
214 |
Failure |
96 |
121 |
98 |
Test whether the proportions are equal for each category at the α = 0.01 level of significance.
ANSWER:
Answer:
Step 1 of 2
For this analysis, the significance level is 0.01. Using sample data, we will conduct a chi-square test for independence.
Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.
DF = (r - 1) * (c - 1) = (2 - 1) * (3 - 1) = 2
|
Category 1 |
Category 2 |
Category 3 |
Total |
Success |
204 |
199 |
214 |
617 |
Failure |
96 |
121 |
98 |
315 |
Total |
300 |
320 |
312 |
932 |
= 198.61
= 211.54
= 206.54
= 101.39
= 108.15
= 105.45
The calculation continues as follows. Letting E be the expected frequency of an outcome and O be the observed frequency of that outcome, compute
O |
E |
(O - E)2 |
(O-E)2/E |
|
200 |
198.61 |
1.9321 |
0.009728 |
|
199 |
211.54 |
157.2516 |
0.743366 |
|
214 |
206.54 |
55.6516 |
0.269447 |
|
96 |
101.39 |
29.0521 |
0.286538 |
|
121 |
108.15 |
165.1225 |
1.526791 |
|
98 |
105.45 |
55.5025 |
0.526339 |
|
SUM |
928 |
931.68 |
464.5124 |
3.36221 |