Question

An on-line retailing firm conducts a study into the number of on-line purchases of footwear made during all of last year. The study wants to determine the proportion of Australians over the age of 25 who purchase footwear on-line. The managing director of the on-line retailing firm believes this proportion of Australians is 18%. A random sample of 180 Australians over the age of 25 is selected. If the managing director’s claim is true, what is the sample proportion value below which 10% of all sample proportions would exist? Express your answer correct to two decimal places

Answer 1

Solution:

We are given:

We first need to find the z-value corresponding to area = 0.10. Using the standard normal table, we have:

Now using the z-score formula, we have:

Therefore, the sample proportion value below which 10% of all sample proportions would exist is 0.14