Suppose 3% of students drink more than 3 cups…

Question

Suppose 3% of students drink more than 3 cups of coffee each day. To check this claim, a researcher randomly selected a sample of 124 students and found that 5 drink more than 3 cups of coffee each day. What is the sampling distribution of the sample proportion? (Round to 2 decimal places for all z-values and round all other answers to 4 decimal places, if needed.) 

The distribution of the sample proportion of students drinking more than 3 cups of coffee each day _____(b1) with a mean of _______ and a standard deviation of _______.

(b1) options: (is approximately normal) or (may not be normal)

Answer 1

This is not an answer to the student but to the professor who put the question together!!

This is a terribly misleading question!

You set up a situation where a number of samples are taken with dichotomous outcomes (GT 3 cups/day or LE 3 cups per day). This is a classic binomial distribution. which has parameters of p and n. Then you set up a situation where the student is lead to believe that a normal distribution is involved by asking for a mean and standard deviation, which are parameters for a normal distribution. Not a binomial.

Trying to justify the use of a simplifying / approximation solution and using a normal approximation is also wrong as the p value is very low (only .0403 using the typical biased estimator of s/n). This is ridiculously low and fails all the standard tests (test 1" When n * p and n * q are greater than 5 you can use approximation". n*p =5 so it fails) (test 2 " when np(1 − p) > 10" you can use normal approximation: n*p*q = 4.79 which also fails). So trying to trick the student into using a normal approximation with leading questions only produces confusion and bad results.

My advice to the student. Refuse to answer the question as phrased.

The distribution is binomial with a p of either 0.0403(biased) or .04 (unbiased Laplace estimate), with an n of 124. Normal approximation is not justified due to sample size and low p.

Answer 2

Hi Mish L.,

You've asked 7 questions, in great detail, on the same skill set, all at the same time, without evidence you've even thought about the problems? That's spamming. Doing your entire problem set for you is first, forbidden under Wyzant rules, and second, won't help you acquire the skills you need. Ask one question, digest the lesson, and do the rest yourself -- that would be appropriate.

-- Cheers, --Mr. d.