QSO 510 :module 2 Essay Example
QSO 510: Module 2 Homework
Notes:
1. Before doing this assignment, do the practice problem posted under Apply and Discover.
2. Word-process your solutions within this template. Do not create a new file.
3. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.
4. Word-process formulas using Equation Editor and diagrams using Drawing Tool.
Problem 1
If many samples of size 15 (that is, each sample consists of 15 items) were taken from a large normal population with a mean of 18 and variance of 5, what would be the mean, variance, standard deviation and shape of the distribution of sample means? Give reasons for your answers.
Note: Variance is the square of the standard deviation.
Adapted from Statistics for Management and Economics by Watson, Billingsley, Croft and Huntsberger. Fifth Edition. Chapter 7 Page 308. Allyn and Bacon. 1993 μx = 18 σ2x=5 shape = normal
Therefore, σx= √σ2x = √5 = 2.2360
If a large number of samples, each of size 15, are selected from the population and a sample mean is selected computed for each sample, the mean, variance and shape of the distribution of sample means would be as follows: μx= 18
The standard deviation of sample means σx̅ can be computed as given below: σx̅ = σX = 2.2360 = 0.5773 √n √15
Variance is the square of the standard deviation. Therefore, the variance of the sample means σ²x̅ can be computed as follows: σ²x̅ = σ²x = 5 = 0.3333 n 15
Shape of the distribution of sample means = normal since sample size n ≥ 30
Problem 2
If many samples of size 100 (that is, each sample consists of 100 items) were taken from a large non-normal population with a mean of 10 and variance of 16, what would be the mean, variance, standard deviation and shape of the distribution of sample means? Give reasons for your answers.
Note: Variance is the square of the standard deviation.
Adapted from Statistics for
Notes:
1. Before doing this assignment, do the practice problem posted under Apply and Discover.
2. Word-process your solutions within this template. Do not create a new file.
3. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.
4. Word-process formulas using Equation Editor and diagrams using Drawing Tool.
Problem 1
If many samples of size 15 (that is, each sample consists of 15 items) were taken from a large normal population with a mean of 18 and variance of 5, what would be the mean, variance, standard deviation and shape of the distribution of sample means? Give reasons for your answers.
Note: Variance is the square of the standard deviation.
Adapted from Statistics for Management and Economics by Watson, Billingsley, Croft and Huntsberger. Fifth Edition. Chapter 7 Page 308. Allyn and Bacon. 1993 μx = 18 σ2x=5 shape = normal
Therefore, σx= √σ2x = √5 = 2.2360
If a large number of samples, each of size 15, are selected from the population and a sample mean is selected computed for each sample, the mean, variance and shape of the distribution of sample means would be as follows: μx= 18
The standard deviation of sample means σx̅ can be computed as given below: σx̅ = σX = 2.2360 = 0.5773 √n √15
Variance is the square of the standard deviation. Therefore, the variance of the sample means σ²x̅ can be computed as follows: σ²x̅ = σ²x = 5 = 0.3333 n 15
Shape of the distribution of sample means = normal since sample size n ≥ 30
Problem 2
If many samples of size 100 (that is, each sample consists of 100 items) were taken from a large non-normal population with a mean of 10 and variance of 16, what would be the mean, variance, standard deviation and shape of the distribution of sample means? Give reasons for your answers.
Note: Variance is the square of the standard deviation.
Adapted from Statistics for