To compare the mean of the population to the mean of the sampling distribution of the sample mean, let's start with some important statistical principles:

• The mean of the population (often denoted as μ) refers to the average value of all elements in a population.
• The mean of the sampling distribution of the sample mean (also called the expected value of the sample mean, denoted as $\mu_{\bar{x}}$) refers to the average of the sample means from all possible samples of the same size from the population.

According to the Central Limit Theorem, the mean of the sampling distribution of the sample mean is equal to the mean of the population, i.e.,

$\mu_{\bar{x}} = \mu$

This means that:

• The mean of the population is equal to the mean of the sampling distribution of the sample means.

Thus, you would answer:

• The mean of the population, μ, is equal to the mean of the sample means, μₓ̄.

If you need to round this to two decimal places, you would round the actual population mean or sample mean values provided in your data set (if any) to two decimal places. Since no specific values are given here, I cannot do that rounding, but I can assist further if you provide the actual population mean.

Would you like me to clarify anything, or do you have specific data for this problem?

Here are some follow-up questions for deeper understanding:

1. What is the Central Limit Theorem and why does it matter in statistics?
2. How does sample size affect the sampling distribution of the sample mean?
3. What is the difference between the population mean and the sample mean?
4. What happens to the standard deviation of the sample mean as sample size increases?
5. Why do we often use samples instead of studying entire populations?

Tip: The shape of the sampling distribution of the sample mean becomes approximately normal as the sample size increases, regardless of the population distribution.