Question

The baseball players salaries from the 2015 season have a population mean μ = 4.215 million dollars and the population standard deviation σ = 5.481 million dollars.

1. Use Equation standard Deviation/ √n  to determine the mean and the standard deviation of the sampling distribution of sample means of n randomly selected baseball players where (i) n = 15 and n = 100.

2. What happened to the mean and the standard deviation of the sampling distribution as the sample size increased? Explain why your response makes sense.

Answer 1

From the given information,

Mean= 4.215

Sd= 5.481

Now,

By using calculator,

i. For n= 15

Mean= 4.215

Sd= 1.415

ii. For n= 100

Mean= 4.215

Sd= 0.548

Hence, As mean of sampling distribution is independent of sample size, it does not changes with sample size but standard deviation of sampling distribution is inversely proportional to sample size hence standard deviation of sampling distribution decreases as sample size increases and vice versa.