Calculate the appropriate statistic for a chi-square test for homogeneity or independence.
Example Problems
A summer swim coach wondered whether preferred competition stroke was related to swimmer age group. They surveyed a random sample of 150 swimmers. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):
They want to use these results to carry out a test of independence. Assume that all conditions for inference were met.
What is the value of the test statistic for their test?
| Chi-square test: Preferred stroke vs. age group | ||||
|---|---|---|---|---|
| Freestyle | Backstroke | Butterfly | Total | |
| Under 16 | 45 | 30 | 15 | 90 |
| 36 | 36 | 18 | ||
| 16 and older | 15 | 30 | 15 | 60 |
| 24 | 24 | 12 | ||
| Total | 60 | 60 | 30 | 150 |
They want to use these results to carry out a test of independence. Assume that all conditions for inference were met.
What is the value of the test statistic for their test?
A school newspaper club wondered whether the frequency of TikTok use varied by grade level. They surveyed a random sample of 200 students. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):
Chi-square test: TikTok use frequency vs. grade level
They want to use these results to carry out a test of independence. Assume that all conditions for inference were met.
What is the value of the test statistic for their test?
Chi-square test: TikTok use frequency vs. grade level
| 9th grade | 10th grade | 11th grade | Total | |
|---|---|---|---|---|
| Uses daily | 60 | 30 | 30 | 120 |
| 48 | 36 | 36 | ||
| Does not use daily | 20 | 30 | 30 | 80 |
| 32 | 24 | 24 | ||
| Total | 80 | 60 | 60 | 200 |
They want to use these results to carry out a test of independence. Assume that all conditions for inference were met.
What is the value of the test statistic for their test?
A coffee shop manager wondered whether customer drink choice depended on time of day. They tracked a random sample of 200 orders during one week. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):
They want to use these results to carry out a test of independence. Assume that all conditions for inference were met.
What is the value of the test statistic for their test?
| Chi-square test: Time of day vs. drink choice | ||||
|---|---|---|---|---|
| Hot coffee | Iced coffee | Tea | Total | |
| Morning | 40 | 25 | 15 | 80 |
| 32 | 24 | 24 | ||
| Afternoon | 25 | 30 | 25 | 80 |
| 32 | 24 | 24 | ||
| Evening | 15 | 5 | 20 | 40 |
| 16 | 12 | 12 | ||
| Total | 80 | 60 | 60 | 200 |
They want to use these results to carry out a test of independence. Assume that all conditions for inference were met.
What is the value of the test statistic for their test?
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