MATHEMATICS HIGH SCHOOL

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 334 people living in East Vancouver and finds that 43 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?

Answers

Answer 1
Answer:

Answer:

The sample should be as large as 480

Step-by-step explanation:

Probability of having a flu, p = 43/334

p = 0.129

Margin Error, E = 0.03

Confidence Interval, CI= 95%

At a CI of 95%, z_(crit) = 1.960

The sample size can be given by the relation:

n = p(1-p)(z/E)^(2)

n = 0.129(1-0.129)(1.960/0.03)^(2) \nn = 479.59\nn = 480
Answer 2
Answer:

Final answer:

To determine the sample size needed to estimate the population proportion with a desired margin of error, we can use the formula n = (z^2 * p * (1-p)) / (E^2), where n is the required sample size, z is the z-score corresponding to the desired level of confidence, p is the estimated proportion of the population with the characteristic, and E is the desired margin of error. Plugging in the given values, the epidemiologist should take a sample size of approximately 3245 in order to achieve her desired margin of error.

Explanation:

To determine the sample size needed to estimate the population proportion with a desired margin of error, we can use the formula:

n = (z^2 * p * (1-p)) / (E^2)

Where:

  • n is the required sample size
  • z is the z-score corresponding to the desired level of confidence (in this case, 95% confidence)
  • p is the estimated proportion of the population with the characteristic (in this case, the proportion of people with the flu in East Vancouver)
  • E is the desired margin of error (in this case, 0.03)

Plugging in the given values:

n = (z^2 * p * (1-p)) / (E^2) = (1.96^2 * 0.129 * 0.871) / (0.03^2) ≈ 3244.42

So, the epidemiologist should take a sample size of approximately 3245 in order to achieve her desired margin of error.

Learn more about Calculating Sample Size here:

brainly.com/question/34288377

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Answers

Answer:

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