Patrick is a health researcher. He wonders if emergency room visits are evenly distributed across the days of the week. He plans to take a random sample of recent visits in order to carry out a [tex]\chi^2[/tex] goodness-of-fit test on the results. What is the smallest sample size Patrick can take to pass the large counts condition?

Question

17-05-2025
Mathematics

High School

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Patrick is a health researcher. He wonders if emergency room visits are evenly distributed across the days of the week. He plans to take a random sample of recent visits in order to carry out a [tex]\chi^2[/tex] goodness-of-fit test on the results. What is the smallest sample size Patrick can take to pass the large counts condition?

Answer :

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hemalatharaja201 hemalatharaja201 · Answer 1 · 2024-01-25T06:56:50-05:00

Patrick should have a total sample size of at least 35 to satisfy the large counts condition for the chi-square goodness-of-fit test, assuming emergency room visits are evenly distributed across the 7 days of the week.

Patrick, a health researcher, wants to ensure that the sample size is large enough to satisfy the large counts condition for a chi-square (x²) goodness-of-fit test. To pass the large counts condition, each expected frequency in the test should be at least 5. Since Patrick is checking if emergency room visits are evenly distributed across the 7 days of the week, and assuming the null hypothesis that they are equally likely, each day should have an expected frequency of at least 5. Therefore, Patrick should have a total sample size of at least 35 (7 days * 5 patients), to ensure each day can be expected to have the minimum number of visits. If Patrick expects differently distributed visits across the days of the week based on prior data, he would need to adjust the sample size accordingly to ensure that the least frequent day still has an expected count of at least 5.