2 points refer to the following scenario an epidemiologist...

(2 points) Refer to the following scenario. 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 336 people living in East Vancouver and finds that 37 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.

Transcript

00:01 Okay, and your question, you're told that there was a study conducted a simple random sample of 336 people and 37 recently had the flu.

00:11 That gives us an estimate for the true population proportion of people that had the flu recently.

00:20 Now, i changed that to a decimal, and your question says carry that to six decimal places.

00:25 So i'm going to try to carry that through my work when i use it.

00:28 Ultimately, your question is saying that we're trying to.

00:31 To work with a 95 % confidence interval, and we're interested in having a margin of error of 0 .03, no larger than that, what sample size should we select for a follow -up sample? so margin of error is found by taking a critical value times your standard error for the sampling distribution.

00:53 That works out to be critical value is typically called z star, and your standard error formula is as shown for sampling distributions of sample proportions.

01:03 So margin of error, we know we want to be 0 .03.

01:11 Your critical value, z star, is really one you want to memorize for a 95 % confidence level.

01:19 It's 1 .96.

01:21 Where it comes from is in a normal distribution.

01:27 The z star value is the z score that blocks off the middle 95 % of the data.

01:35 So if i needed to look that up, i would have to include the 2 .5 % that's in the left tail so that i look at z table correctly.

01:49 And that's going to be 0 .975 that i look up.

01:55 So if i look at a z table for 0 .975, i see it right there.

02:00 That happened at 1 .96...