Question

Suppose that we will randomly select a sample of 82 measurements from a population having a mean equal to 24 and a standard deviation equal to 3. a. Describe the shape of the sampling distribution of the sample mean. b. Calculate the standard error of the sample mean.

Answer 1

a. The sampling distribution of the sample mean is approximately normally distributed when the sample size is sufficiently large. b. The standard error of the sample mean can be calculated using the formula: σ/√n.

Step-by-step explanation:

a. The sampling distribution of the sample mean is approximately normally distributed when the sample size is sufficiently large. This is known as the Central Limit Theorem.

In this scenario, we have a sample size of 82, which is large enough to assume a normal distribution.

b. The standard error of the sample mean can be calculated using the formula: σ/√n, where σ is the population standard deviation and n is the sample size.

In this case, the standard error of the sample mean is 3/√82, which is approximately 0.3323 when rounded to two decimal places.