Calculate the appropriate statistic for the chi-square test for goodness of fit.
Example Problems
Owen wondered whether the goals scored across the four quarters of his school's soccer games had an even distribution, so he took a random sample of 120 goals from past games and recorded the quarter in which each goal was scored. Here are his results:
He wants to use these results to carry out a goodness-of-fit test to determine if the distribution of goals across quarters disagrees with an even distribution.
What is the value of the test statistic for Owen's test?
| Quarter | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|
| Goals | 22 | 28 | 34 | 36 |
He wants to use these results to carry out a goodness-of-fit test to determine if the distribution of goals across quarters disagrees with an even distribution.
What is the value of the test statistic for Owen's test?
Coach Reed wondered whether the shots her basketball team took during a game had an even distribution across four zones (paint, mid-range, corner three, top three), so she took a random sample of 200 shots from this season and recorded their zones. Here are her results:
She wants to use these results to carry out a goodness-of-fit test to determine if the distribution of shot zones disagrees with an even distribution.
What is the value of the test statistic for Coach Reed's test?
| Zone | Paint | Mid-range | Corner three | Top three |
|---|---|---|---|---|
| Shots | 60 | 45 | 55 | 40 |
She wants to use these results to carry out a goodness-of-fit test to determine if the distribution of shot zones disagrees with an even distribution.
What is the value of the test statistic for Coach Reed's test?
Owen wondered whether the goals scored across the four quarters of his school's soccer games had an even distribution, so he took a random sample of 120 goals from past games and recorded the quarter in which each goal was scored. Here are his results:
He wants to use these results to carry out a goodness-of-fit test to determine if the distribution of goals across quarters disagrees with an even distribution.
What is the value of the P-value for Owen's test?
Round your answer to the nearest thousandth.
| Quarter | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|
| Goals | 22 | 28 | 34 | 36 |
He wants to use these results to carry out a goodness-of-fit test to determine if the distribution of goals across quarters disagrees with an even distribution.
What is the value of the P-value for Owen's test?
Round your answer to the nearest thousandth.
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