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?

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

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

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

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

E.Yes, the random condition for finding confidence intervals is met because the sample is a simple random sample.

Answer 1

Yes, the random condition for finding confidence intervals is met because the sample is a simple random sample.

Explanation:

This is the correct answer, I took the quiz and got it right.

Answer 2

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

E. Yes, the random condition for finding confidence intervals is met because the sample is a simple random sample.

Explanation:

In order for the random conditioning to be valid, the following must be met:

1. the sample taken is a simple random sample, i.e. each student had the same probability of being surveyed
2. the sample size was sufficiently large, i.e. both np and n(1 - p) are larger than 10.

Since both conditions are met, then the confidence interval is valid. A valid confidence interval is one that has 95% chance of containing the total population's parameters.