Solution Found!
The table in the next column contains observed values and
Chapter , Problem 4AYU(choose chapter or problem)
Problem 4AYU
The table in the next column contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories
|
X1 |
X2 |
X3 |
Y1 |
87 (75.12) |
74 (80.43) |
34 (39.46) |
Y2 |
12 (23.88) |
32 (25.57) |
18 (12.54) |
(a) Compute the value of the chi-square test statistic.
(b) Test the hypothesis that X and Y are independent at the α = 0.05 level of significance.
Questions & Answers
QUESTION:
Problem 4AYU
The table in the next column contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories
|
X1 |
X2 |
X3 |
Y1 |
87 (75.12) |
74 (80.43) |
34 (39.46) |
Y2 |
12 (23.88) |
32 (25.57) |
18 (12.54) |
(a) Compute the value of the chi-square test statistic.
(b) Test the hypothesis that X and Y are independent at the α = 0.05 level of significance.
ANSWER:
Answer:
Step 1 of 1
(a) 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 |
|
87 |
75.12 |
141.1344 |
1.878786 |
|
74 |
80.43 |
41.3449 |
0.514048 |
|
34 |
39.46 |
29.8116 |
0.755489 |
|
12 |
23.88 |
141.1344 |
5.910151 |
|
32 |
25.57 |
41.3449 |
1.61693 |
|
18 |
12.54 |
29.8116 |
2.377321 |
|
Sum |
257 |
424.5818 |
13.05272 |
The Test Statistic is given by
Therefore, is the required test statistic.