2. You have been hired to do market research, and you must estimate the percentage of households in which at least one plant is being grown. How many households must you survey if you want to be 95% confident that your sample percentage is three percentage points higher than what has been estimated previously in the literature? A previous study suggested that plants are grown in 86% of households. Assume a two-tail test and a type II error of 10%.

a) How many households will you need to survey in your study to test your hypothesis?

b) Lets say that you were able to recruit 700 households in the study. Keeping all other specifications fixed, what would be the power of your study?

c) Explain how the concept of statistical power is associated with sample size?

d) Provide SAS syntax and outputs for parts a-b