Question

Suppose that at Northside High, the number of hours per week that seniors spend on homework is approximately Normally distributed with a mean of 18.6 and a standard deviation of 6.0. We take a simple random sample of 36 seniors and calculate the sample mean homework hours per week. What is the mean of the sampling distribution of means for the 36 students

Answer 1

Answer:

The mean of the sampling distribution of means for the 36 students is of 18.6 homework hours per week.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

For the population, the mean is 18.6. So, by the Central Limit Theorem, the mean of the sampling distribution is also 18.6.