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 2 of 2: If a sampling distribution is created using samples of the ages at which 38 children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.

Answer 1

Explanation:

The standard deviation of the sampling distribution of sample means is given by the formula:

standard deviation = population standard deviation / sqrt(sample size)

Here, the population standard deviation is 0.8 years, and the sample size is 38. Substituting these values into the formula, we get:

standard deviation = 0.8 / sqrt(38)

standard deviation ≈ 0.13

Rounding to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.13 years.