Question

For the following four questions, is it appropriate to use a normal distribution to approximate a confidence interval for the population proportion? If it’s inappropriate, indicate why.

A clothing store owner wants to know the proportion of customers who used coupons within the last year. He selects in a random order all 2,000 receipts from a database of all purchases within the last year and finds that 340 of them are discounted by coupons.

Select one:

a. Yes.

b. No, because it wasn't a random sample.

c. No, because n(p-hat) < 10 or n(q-hat) < 10.

d. No, because the sample size wasn’t at least 30 and the population wasn’t normally distributed.

e. No, because we already know the population proportion.

Answer 1

Solution

He selects a random sample

n = 2000

x = 340

phat = 340/2000 = 0.17

nphat = 340

n(qhat) = 1660

Both greater than 10.

All conditions are satisfied.

Answer is YES

It is appropriate to use the normal distribution