AP Statistics Class

Question

Leon wants to estimate the proportion of the seniors at his high school who like to watch football. He interviews a simple random sample of 50 of the 200 seniors on campus. He finds that 32 like to watch football. Is the random condition for finding confidence intervals met? Explain.

Yes, the random condition for finding confidence intervals is met because np̂ = 32 and n(1 − p̂) = 18, both of which are greater than 10. 

Yes, the random condition for finding confidence intervals is met because the sample size is greater than 30.

 No, the random condition for finding confidence intervals is not met because np̂ = 32 and n(1 − p̂) = 18, both of which are less than 100.

 No, the random condition for finding confidence intervals is not met because the sample is not at least 50% of the population. Yes, the random condition for finding confidence intervals is met because the sample is a simple random sample

Answer 1

Confidence interval approach is valid if 1) sample is a simple random sample and 2) sample size is sufficiently large, i.e., includes at least 10 successes and 10 failures. Those two conditions are met by the sample described.