Let's go over each question in detail.

Question 2

The population mean for Verbal IQ scores is 100, with a standard deviation of 15. Suppose a researcher takes 50 random samples, with 30 people in each sample.
What is the mean of the sample means?

The mean of the sample means, also known as the expected value of the sampling distribution of the sample mean, will always be equal to the population mean. This is a result of the Central Limit Theorem.

So, the answer is:

• 100

Question 3

The sampling distribution of a statistic is (select the best answer):

1. The mechanism that determines whether the random sampling was effective.
2. A normal curve, for which probabilities are obtained by standardizing.
3. A distribution of all parameters from the population that is to be randomly sampled.
4. A distribution of a single statistic from repeated random samples of the same size, from the same population.
5. A distribution of all possible summary statistics from a single random sample, from the same population.

The best answer here is:

• A distribution of a single statistic from repeated random samples of the same size, from the same population.

The sampling distribution is essentially the distribution of a particular statistic (e.g., the mean) calculated from multiple random samples of the same size from the population.

Would you like further details on any part of the solution?

Follow-up Questions:

1. What is the Central Limit Theorem, and how does it apply to sampling distributions?
2. How does sample size affect the standard deviation of the sampling distribution?
3. Why is the mean of the sampling distribution equal to the population mean?
4. In what cases would a sampling distribution not be approximately normal?
5. How would you calculate the standard error for a sample mean?

Tip:

Remember, the sampling distribution of the mean becomes approximately normal if the sample size is large enough, even if the population distribution is not normal. This is due to the Central Limit Theorem.