Question

Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.3 years with a standard deviation of 1.1 years.

Step 2 of 2: If a sampling distribution is created using samples of the ages at which 35 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

The standard deviation of the sampling distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:

standard error = standard deviation / square root of sample size

In this case, the standard deviation of the population is 1.1 years, and the sample size is 35. Substituting these values into the formula, we get:

standard error = 1.1 / sqrt(35) ≈ 0.186

Rounding to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.19 years.

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Explanation: