Question

A marketing consultant wants to estimate the true proportion of all residents that live near a certain mall who make at least one purchase at the mall in the past week. He stands at a mall exit for two hours on a weekday afternoon and flips a coin each time a shopper leaves. If the coin comes up heads, he asks them if they have made any purchases during this visit. After two hours, he has 132 responses, 104 of whom made a purchase. Which condition for constructing a confidence interval for a proportion has the consultant failed to satisfy

Answer 1

Options :

a) np ≥ 10

b) n(1-p ) ≥ 10

c) n ≥ 30

d) The data is a random sample from the population of interest.

e) The sample is less than 10% of the population.

Answer:

d) The data is a random sample from the population of interest.

Explanation:

To construct a confidence interval, certain conditions has to be met before the validity of the confidence interval could be established, this include a sufficiently large sample, (n > 30)

n (1- p) ≥ 10 = 132(1 - 104/132) = 132 * 0.2121 = 28 (condition is met).

The condition which the data fail to meet is the randomization condition, whereby the method of selection isn't completely random with some participants having a much more chances of being selected ahead of others. A better random sampling procedure should be is d in the population to draw out the required sample.