Question

4. The annual per capita consumption of sugar by people in the US is a right skewed distributed with a mean of 152 pounds a standard deviation of 18.2 pounds. Random samples of size 60 are drawn from this population, and the mean of each sample is determined.

a. Using Central Limit Theorem, what would the mean, standard deviation, and shape of the sampling distribution be?
b. Now assume that random samples of size 120 are drawn instead. What would the mean, standard deviation and shape of the sampling distribution be? Which measures changed and how would they change?

Answer 1

Explanation:

a. According to the Central Limit Theorem, sufficiently large random samples from a population are approximately normally distributed, even if the population itself isn't normally distributed.

By "sufficiently large", we usually mean at least 30.

The sample mean is μ = 152.

The sample standard deviation is σ = 18.2 / √60 ≈ 2.35.

b. The mean and shape are the same. The standard deviation decreases to:

σ = 18.2 / √120 ≈ 1.66.