Question 20 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
In a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. The students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. For one student, it lands tails side up six times. The student will construct a 90% confidence interval for the true proportion of tails up. Are the conditions for inference met?
Answer
A
Yes, the conditions for inference are met.
B
No, the 10% condition is not met.
C
No, the randomness condition is not met.
D
No, the Large Counts Condition is not met.
Explanation
For a one-proportion confidence interval, the Large Counts Condition requires at least 10 successes and 10 failures. The student observed 6 tails and 4 non-tails in 10 spins, so both counts are below 10. Therefore, the Large Counts Condition is not met, and a 90% confidence interval using this method is not justified.
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