Question

We measured the weight of 30 rats under experiment controls. Suppose that 12 were underweight rats. Let p be the population proportion. What sample size is needed to be 95% confident that the error in estimating the true proportion of rats that are underweight is less than 2%?

a. 300
b. 429
c. 496
d. 625

Answer 1

To estimate the true proportion of underweight rats with a 95% confidence level and an error less than 2%, a sample size of 430 is needed.

Step-by-step explanation:

To determine the sample size needed to estimate the true proportion of underweight rats with a 95% confidence level and an error less than 2%, 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 confidence level (in this case, 1.96 for a 95% confidence level), p is the estimated proportion (12/30 = 0.4), and E is the desired error (0.02).

Plugging in the values, we get:

n = (1.96^2 * 0.4 * (1-0.4)) / (0.02^2) = 429.926

Rounding up, the minimum sample size needed is 430.