Question

An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 332 people living in East Vancouver and finds that 39 have recently had the flu. Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to have a margin of error no larger than 0.03. How large a sample should she take to achieve this? Please carry answers to at least six decimal places in intermediate steps.

Calculate the sample size:

Sample size =

Answer 1

Step1: The minimum sample size required to estimate the population proportion. The Margin of error E 0.03 The confi dence level is a 0.05 Step2: The sample proportion isp-- 39 332 p0.11747 1- 0.11747 0.88253 Step3: The formula for calculating the sample size is 0.11747) (1-0.11747) 0.03 1.96 003 (0.11747)(0 88253) (65.33333)' (0.11747) (0.88253) (4268.444) (0.103671) 442.5127 443 Step4: Therefore, the sample size needed to estimate the populati on proportion is approxim atelyn443