Answer :
The final answer is a sample size of 50 rolls.
1. Large Counts Condition:
- In order to perform a chi-square goodness-of-fit test, each expected count in the contingency table should be at least 5, according to the large counts condition.
- Since Miriam has a 10-sided die, there are 10 possible outcomes.
- To ensure each expected count is at least 5, she needs a total of at least [tex]\(10 \times 5 = 50\)[/tex] rolls.
2. Explanation:
- Suppose Miriam rolls the die [tex]\(n\)[/tex] times.
- The expected count for each side would ideally be [tex]\(n/10\)[/tex] since there are 10 sides and the die is fair.
- For the large counts condition, each expected count should be at least 5.
- Therefore, [tex]\(n/10 \geq 5\)[/tex] .
- Solving for [tex]\(n\)[/tex], we get [tex]\(n \geq 50\)[/tex] .
- Thus, the smallest sample size Miriam can take to pass the large counts condition is 50 rolls.
