Based on past data, it is known that about 8.96% of people who go to the doctor end up testing positive for influenza. Suppose we take a sample of 100 doctor visits and find that 9.17% of people test positive for influenza. We want to see if there is evidence that the percentage of people who have influenza is increasing.
If I wanted to control my margin of error and set it to 3% with 99% confidence, what sample size would I need to take instead of the 100?
Using my original sample size of 100, what would be the 99% confidence interval for the population proportion?
What are the null and alternative hypotheses?
What is the critical value at 99% confidence?
Calculate the test statistic (using the sample of 100).
Find the p-value.
What conclusion would be made here at the 99% confidence level?