Calculate expected counts for the chi-square test for goodness of fit.
Example Problems
Talia designed a spinner divided into seven equal segments. She spun it 350 times and recorded how often each segment was hit.
Talia wants to perform a goodness-of-fit test to determine if these results suggest that the spinner lands on one specific segment more often than the others.
What is the expected count of hits for segment 5?
| Segment | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Observed hits | 52 | 46 | 53 | 45 | 47 | 54 | 53 |
Talia wants to perform a goodness-of-fit test to determine if these results suggest that the spinner lands on one specific segment more often than the others.
What is the expected count of hits for segment 5?
Priya manages 3 pickleball courts at the community center. She wonders if players reserve some courts more often than others when given a choice. She records which court was chosen first across 360 reservations. Here are the results:
Priya wants to perform a goodness-of-fit test to determine if these results suggest that players reserve one specific court more often than the others.
What is the expected count of reservations at the second court?
| Court | #1 | #2 | #3 |
|---|---|---|---|
| Observed reservations | 132 | 108 | 120 |
Priya wants to perform a goodness-of-fit test to determine if these results suggest that players reserve one specific court more often than the others.
What is the expected count of reservations at the second court?
At a Pokémon trading card club, members can choose one of 4 starter packs at each meeting. The club president wonders if members pick some starters more often than others. She records the choice across 240 meetings. Here are the results:
She wants to perform a goodness-of-fit test to determine if these results suggest that members pick one specific starter more often than the others.
What is the expected count of picks for Electric?
| Starter | Grass | Fire | Water | Electric |
|---|---|---|---|---|
| Observed picks | 68 | 58 | 64 | 50 |
She wants to perform a goodness-of-fit test to determine if these results suggest that members pick one specific starter more often than the others.
What is the expected count of picks for Electric?
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