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Generating the sampling distribution of M


Complete: Chapter 7 Problem Set Back to Assignment Average: /6 Attempts: A Aa 3. Generating the sampling distribution of M Le

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_______ .




Solutions

Expert Solution

μ = 55/10

= 5.5

  

σ = 2.87

μM = 5.5 = μ

σM = 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


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