a. to find p^, which represents the proportion of people who tested positive, we use the formula: p^ = number who tested positive / total number tested. given that 19 people tested positive out of 228 tested, we have: p^ = 19 / 228 = 0.0833, rounded to the nearest hundredth of a percent, p^ is approximately 8.33%.
b. to estimate the number of people who would test positive for the virus among the 23,000 people living in the radius, we use the proportion calculated in part a: number of people who would test positive = p^ * total population = 0.0833 * 23,000 = 1,916.9. rounded to the nearest whole number, the best estimate is that approximately 1,917 people would test positive for the virus.
c. to ensure that the testing results are not biased, the county could implement several measures: random sampling to ensure that the individuals selected for testing are chosen randomly from the population to avoid selection bias, control for confounding variables by considering and controlling for factors that could influence the test results, such as age, gender, or pre-existing health conditions, use reliable testing methods to ensure that the testing methods used are accurate and validated to minimize errors in diagnosis, transparent reporting by providing clear and transparent reporting of the testing process, including sample size, methodology, and any limitations or biases that may exist.
