Answer :
The smallest sample size Patrick needs to satisfy the large counts condition for a goodness-of-fit test across 7 days of the week is Option B) 50, as each expected frequency must be at least 5.
Patrick, a health researcher, wants to check if emergency room visits are evenly distributed across the week days using a goodness-of-fit test. For such a test, the large counts condition asserts that all expected counts must be at least 5. Since there are 7 days of the week, we would want our sample size to be large enough so that the expected frequency for each day is at least 5. To achieve this, we would calculate the smallest sample size by multiplying the number of categories (7 days) by the minimum expected frequency (5), which gives us [tex]7 \times 5 = 35[/tex]. However, the available options do not include 35, so the next highest available option that satisfies this condition is 50. Therefore, option B. 50 is the correct answer.
