Question

If a sampling distribution is created using samples of the ages of 55 children begin reading what would be the standard deviation of the sampling distribution of sample means Round answer to two decimal places

Answer 1

2)We have a population with mean 5.7 years and standard deviation 0.7 years.

When we have a sampling distribution (distribution of the sample means) for a sample with size n, its mean and standard deviation will be:

`\begin{gathered} \mu_s=\mu \\ \\ \sigma_s=(\sigma)/(√(n)) \end{gathered}`

The mean of the sampling distribution will be equal to the population mean, but the standard deviation will be affected by the sample size.

For a sample size n = 55 and a population standard deviation of 0.7 years we can calculate the sampling distribution standard deviation as:

`\sigma_s=(\sigma)/(√(n))=(0.7)/(√(55))\approx(0.7)/(7.42)\approx0.09`

Answer: the sampling distribution standard deviation is 0.09 years.