Question

A marketing research firm estimates the proportion of potential customers preferring a certain brand of lipstick by selecting a sample of 100 women who come by their booth in a shopping mall on a specified day. Of the 100 sampled, 65 women stated a preference for brand A.
a. What is the target population of this study?
b. Did the marketing research firm select a simple random sample?
c. Assume this is a random sample: How would you estimate the true proportion of women preferring brand A with a bound on the error of estimation?

Answer 1

a) Target population for the study are all the women who buy lipsticks.

b) Out of all the women who enter the shop on the specified day, if the probability of selecting any woman is the same as that for any other woman, then the sampling scheme is simple random sampling.

c) The sample proportion 65/100 = 0.65 is an estimate of the true sample proportion of woman preferring brand A.

To have a bound on the error of estimation, a certain minimum sample size should be decided based on the population standard deviation and the maximum acceptable bound.

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