Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.9
years with a standard deviation of 0.7
years.
Step 2 of 2: If a sampling distribution is created using samples of the ages at which 67
children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.
To find the standard deviation of the sampling distribution of sample means, we use the formula:
standard deviation of sampling distribution = standard deviation / sqrt(sample size)
In this case, the standard deviation of the population is 0.7 years and the sample size is 67 children.
standard deviation of sampling distribution = 0.7 / sqrt(67)
standard deviation of sampling distribution ≈ 0.09
Therefore, the standard deviation of the sampling distribution of sample means would be approximately 0.09 years.