Question

Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.4 years with a standard deviation of 0.8 years. Step 1 of 2: If a sampling distribution is created using samples of the ages at which 38 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.

Answer 1

Explanation:

The mean of the sampling distribution of sample means can be calculated using the formula:

μM = μ

where μ is the population mean and M is the sample mean.

Thus, μM = μ = 5.4 years.

Therefore, the mean of the sampling distribution of sample means would also be 5.4 years.

Answer 2

According to the Central Limit Theorem, the sampling distribution of sample means would have a mean of 5.4 years.

Explanation:

For a normally distributed random variable X, with mean and standard deviation, the sampling distribution of sample means with size n can be approximated to a normal distribution with mean and standard deviation.

As long as n is at least 30, the Central Limit Theorem can also be applied to skewed variables.

We have the following problem:

• 5.4 years is the average age for the entire population.
• Based on the Central Limit Theorem, 5.4 years would be the mean of the sampling distribution of sample means.