Question

Veterinarians were interested in learning the true average number of people who adopted animals from the Humane Society. A census study conducted last year found that the population variance was 0.5. How many people would the veterinarians need to sample to achieve a margin of error of no more than 0.03 with a 99% confidence level?

(a) More information is needed to answer this question.

(b) 2135

(c) 1068

(d) 3698

(e) 1849

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 0.03, σ = 0.7071

The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.96 * 0.7071/0.03)^2
n = 2134.18

Therefore, the sample size needed to satisfy the condition n >= 2134.18 and it must be an integer number, we conclude that the minimum required sample size is n = 2135
Ans : Sample size, n = 2135