Question

11. A sample of n = 25 scores has a mean of M = 68. Find the z-score for this sample: a. If it was obtained from a population with μ = 60 and σ = 10. b. If it was obtained from a population with μ = 60 and σ = 20. c. If it was obtained from a population with μ = 60 and σ = 40. 12. A population forms Gravetter, Frederick J. Statistics for The Behavioral Sciences (p. 221). Cengage Learning. Kindle Edition.

Answer 1

Answer:

a) z-score = 4

b) z-score = 2

c) z-score = 1

Step-by-step explanation:

* Lets revise some definition to solve the problem

- The mean of the distribution of sample means is called M

- The standard deviation of the distribution of sample means is

  called σM (standard error)

- σM = σ/√n , where σ is the standard deviation and n is the sample size

- z-score = (M - μ)/σM, where μ is the mean of the population

* Lets solve the problem

∵ The sample size n = 25

∵ The sample mean M = 68

a)

∵ The mean of population μ = 60

∵ The standard deviation σ = 10

- Lets find σM to find z-score

∵ σM = σ/√n

∴ σM = 10/√25 = 10/5 = 2

- Lets find z-score

∵ z-score = (M - μ)/σM

∴ z-score = (68 - 60)/2 = 8/2 = 4

* z-score = 4

b)

∵ The mean of population μ = 60

∵ The standard deviation σ = 20

- Lets find σM to find z-score

∵ σM = σ/√n

∴ σM = 20/√25 = 20/5 = 4

- Lets find z-score

∵ z-score = (M - μ)/σM

∴ z-score = (68 - 60)/4 = 8/4 = 2

* z-score = 2

c)

∵ The mean of population μ = 60

∵ The standard deviation σ = 40

- Lets find σM to find z-score

∵ σM = σ/√n

∴ σM = 40/√25 = 40/5 = 8

- Lets find z-score

∵ z-score = (M - μ)/σM

∴ z-score = (68 - 60)/8 = 8/8 = 1

* z-score = 1