Question

1A. The Madera County Emu Farm wants to start selling t-shirts in addition to emu eggs. The manager wants to sample a few other farms to get a good idea of the average profit that can be made. She wants to be 95% certain of the results, and she wants to be within $1,000 of the true mean. When she was researching online, she found that the standard deviation of the mean t-shirt sales for businesses similar to hers was $2,200. How many emu farms should she get data from? (Remember, our data is discrete.)

B. During the grand opening of the T-Shirt Shack at the Madera County Emu Farm, four of the emus broke through the fence and attacked the customers. The manage of the emu farm is now looking for data about insurance settlements. She has heard that the proportion of settlements that are favorable to businesses is 0.68. She wants to verify this number with her own study. She wants to be 99% confident in her results, and she wants the margin of error to be within 0.1. How many businesses does she need to sample to meet this criteria?

Answer 1

a)

Sample size = (Z$\alpha$/2 * $\sigma$ / E)²

= ( 1.96 * 2200 / 1000)²

= 19 (Rounded up to nearest integer)

b)

Sample size = Z²$\alpha$/2 * p( 1 - p) / E²

= 2.5758² * 0.68 ( 1 - 0.68) / 0.1²

= 145 (Rounded up to nearest integer)