Calculate expected counts for two-way tables of categorical data.
Example Problems
Coach Patel wondered if a basketball team's results depend on whether the game is played at home or away.
He recorded a random sample of games from the season. Here are the results:
He wants to perform a test of homogeneity on these results.
What is the expected count for the cell corresponding to home games that ended in a win?
Round your answer to the nearest hundredth.
He recorded a random sample of games from the season. Here are the results:
| Location | Win | Loss | Total |
|---|---|---|---|
| Home | 18 | 7 | 25 |
| Away | 12 | 13 | 25 |
| Total | 30 | 20 | 50 |
He wants to perform a test of homogeneity on these results.
What is the expected count for the cell corresponding to home games that ended in a win?
Round your answer to the nearest hundredth.
Talia wanted to know if movie genre preference differs between teens and adults.
She surveyed a random sample of 120 moviegoers leaving a multiplex. Here are the results:
She wants to perform a test of homogeneity on these results.
What is the expected count for the cell corresponding to adults who prefer action movies?
Round your answer to the nearest hundredth.
She surveyed a random sample of 120 moviegoers leaving a multiplex. Here are the results:
| Group | Action | Comedy | Drama | Total |
|---|---|---|---|---|
| Teens | 30 | 12 | 8 | 50 |
| Adults | 30 | 18 | 22 | 70 |
| Total | 60 | 30 | 30 | 120 |
She wants to perform a test of homogeneity on these results.
What is the expected count for the cell corresponding to adults who prefer action movies?
Round your answer to the nearest hundredth.
Asha was curious whether the type of volleyball serve is related to the result of the serve.
She recorded a random sample of 100 serves during practice. Here are the results:
She wants to perform a test of independence between serve type and result.
What is the expected count for the cell corresponding to jump serves that were aces?
Round your answer to the nearest hundredth.
She recorded a random sample of 100 serves during practice. Here are the results:
| Serve type | Ace | In | Fault | Total |
|---|---|---|---|---|
| Jump serve | 12 | 16 | 12 | 40 |
| Float serve | 8 | 34 | 18 | 60 |
| Total | 20 | 50 | 30 | 100 |
She wants to perform a test of independence between serve type and result.
What is the expected count for the cell corresponding to jump serves that were aces?
Round your answer to the nearest hundredth.
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