Question

It's known that the weight's standard deviation of the individuals in a population is 6kg. Calculate the size of the sample to considerate, with a 95% confidence level, to estimate the average weight of the individuals in the population with an error inferior to 1kg.​

Answer 1

To find the size of the sample needed to estimate the average weight of individuals in a population with a 95% confidence level and an error of less than 1kg, we can use the following formula:

n = (Z^2 * σ^2) / (e^2)

Where:

n is the sample size

Z is the standard normal deviation corresponding to the confidence level (1.96 for 95% confidence)

σ is the standard deviation of the population (6kg in this case)

e is the desired margin of error (1kg in this case)

Plugging these values into the formula, we get:

n = (1.96^2 * 6^2) / (1^2)

Solving this equation, we get:

n = 38.4

Therefore, the sample size needed to estimate the average weight of individuals in the population with a 95% confidence level and an error of less than 1kg is approximately 38 individuals.