Question

Generating the sampling distribution of M 

Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6, 7,8, 9, and 10 by drawing samples from these values, calculating the mean of each sample, and then considering the sampling distribution of the mean. To do this, suppose you perform an experiment in which you roll a ten-sided die two times (or equivalently, roll two ten-sided dice one time) and calculate the mean of your sample. Remember that your population is the numbers 1, 2, 3, 4, 5, 6, 7,8, 9, and 10. 

The true mean (u) of the numbers 1, 2, 3, 4, 5,6, 7, 8, 9, and 10 is _______ and the true standard deviation (σ) is_______ .

Answer 1

μ = 55/10

= 5.5

  

σ = 2.87

μ_M = 5.5 = μ

σ_M = σ/√n

= 2.87/√2

= 2.03

Total no. of means possilbe = 100

Sample having mean 5.5 = 10

P(M= μ) = 10/100

= 0.1

P(M > 1.5) = 1 - P(M ≤ 1.5)

= 1 - 3/100

= 97/100

= 0.97

Answer 2

the true mean $\mu$ =5.5 and the true standard deviation $\sigma$ is 2.8723

mean of the sampling distribtution $\mu$M would equal 5.5 and standard deviation of your sampling distribution of means $\sigma$M would be 2.0310

P(M=$\mu$) is 0.1 and P(M>1.5)=0.97