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Unformatted text preview: STAT 350 – Fall 2008 Lab #3 – SOLUTION
Sampling Distributions 1. Sidebyside Histograms
a. Give the sidebyside histograms for xN , 25 and xN ,100 .
Histogram of Normal25 mean, Normal100 mean
48
Normal25 mean 40 49 50 51 52 53 Normal100 mean Frequency 30 20 10 0 (i) (ii)
(iii) (iv)
(v) (vi) 48 49 50 51 52 53 What would you have expected the statistic to be (what value)?
I would expect the sample mean to be close to the population mean. The samples
came from a Normal(μ = 50, σ = 5) distribution which has mean 50, so I would
expect the statistic to be 50.
What is the shape of each distribution?
Each distribution is approximately symmetric and bellshaped
What is the center of each distribution (the mean of the distribution, see Step 8 in the
directions)?
Answers will vary because the data was simulated independently by each student, but
answers should be close to 50. For the data graphed above, the centers were 49.962
and 50.012 respectively.
Does the center appear to be affected by increasing the sample size. If so, how?
No – the center was not [significantly] affected by increasing sample size.
What is the standard deviation of each distribution (see Step 8 in the directions)?
Answers will vary because the data was simulated independently by each student, but
5
answers should be close to
(1 and 0.5). For the data graphed above, the standard
n
deviations were 1.017 and 0.507 respectively.
Does the standard deviation appear to be affected by increasing the sample size. If
so, how?
Yes, standard deviation was approximately cut in half when the sample size was
quadrupled Lab #3 – Solution Page 1 of 1 b. Give the sidebyside histograms for sN ,25 and sN ,100 .
Histogram of Normal25 stdev, Normal100 stdev
2.4
Normal25 stdev 40 3.2 4.0 4.8 5.6 6.4 Normal100 stdev Frequency 30 20 10 0 (i) (ii)
(iii) (iv)
(v) (vi) 2.4 3.2 4.0 4.8 5.6 6.4 What would you have expected the statistic to be (what value)?
I would expect the sample standard deviation to be close to the population standard
deviation. The samples came from a Normal(μ = 50, σ = 5) distribution which has
standard deviation of 5, so I would expect the statistic to be 5.
What is the shape of each distribution?
Each distribution is approximately symmetric and bellshaped
What is the center of each distribution (the mean of the distribution, see Step 8 in the
directions)?
Answers will vary because the data was simulated independently by each student, but
answers should be close to 5. For the data graphed above, the centers were 4.8757
and 5.0124 respectively.
Does the center appear to be affected by increasing the sample size. If so, how?
No – the center was not [significantly] affected by increasing sample size.
What is the standard deviation of each distribution (see Step 8 in the directions)?
Answers will vary because the data was simulated independently by each student.
For the data graphed above, the standard deviations were 0.7121 and 0.3821
respectively.
Does the standard deviation appear to be affected by increasing the sample size. If
so, how?
Yes, standard deviation was approximately cut in half when the sample size was
quadrupled Lab #3 – Solution Page 2 of 2 c. Give the sidebyside histograms for xP , 25 and xP ,100 .
Histogram of Poisson25 mean, Poisson100 mean
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8
Poisson25 mean 30 Poisson100 mean Frequency 25
20
15
10
5
0 (i) (ii)
(iii) (iv)
(v) (vi) 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 What would you have expected the statistic to be (what value)?
I would expect the sample mean to be close to the population mean. The samples
came from a Poisson(2) distribution which has mean 2, so I would expect the statistic
to be 2.
What is the shape of each distribution?
Each distribution is approximately symmetric and bellshaped
What is the center of each distribution (the mean of the distribution, see Step 8 in the
directions)?
Answers will vary because the data was simulated independently by each student, but
answers should be close to 2. For the data graphed above, the centers were 2.0428
and 1.9917 respectively.
Does the center appear to be affected by increasing the sample size. If so, how?
No – the center was not [significantly] affected by increasing sample size.
What is the standard deviation of each distribution (see Step 8 in the directions)?
Answers will vary because the data was simulated independently by each student, but
2
(0.2828 and 0.1414). For the data graphed above, the
answers should be close to
n
standard deviations were 0.2959 and 0.1397 respectively.
Does the standard deviation appear to be affected by increasing the sample size. If
so, how?
Yes, standard deviation was approximately cut in half when the sample size was
quadrupled Lab #3 – Solution Page 3 of 3 d. Give the sidebyside histograms for sP ,25 and sP ,100 .
Histogram of Poisson25 stdev, Poisson100 stdev
1.0
Poisson25 stdev 30 1.2 1.4 1.6 1.8 Poisson100 stdev Frequency 25
20
15
10
5
0 (i) (ii)
(iii) (iv)
(v) (vi) 1.0 1.2 1.4 1.6 1.8 What would you have expected the statistic to be (what value)?
I would expect the sample standard deviation to be close to the population standard
deviation. The samples came from a Poisson(2) distribution which has standard
deviation of 2 ≈ 1.414, so I would expect the statistic to be 1.414.
What is the shape of each distribution?
Each distribution is approximately symmetric and bellshaped
What is the center of each distribution (the mean of the distribution, see Step 8 in the
directions)?
Answers will vary because the data was simulated independently by each student, but
answers should be close to 1.414. For the data graphed above, the centers were
1.4120 and 1.4081 respectively.
Does the center appear to be affected by increasing the sample size. If so, how?
No – the center was not [significantly] affected by increasing sample size.
What is the standard deviation of each distribution (see Step 8 in the directions)?
Answers will vary because the data was simulated independently by each student.
For the data graphed above, the standard deviations were 0.2097 and 0.1074
respectively.
Does the standard deviation appear to be affected by increasing the sample size. If
so, how?
Yes, standard deviation was approximately cut in half when the sample size was
quadrupled Lab #3 – Solution Page 4 of 4 2.
Variable
Normal25 mean
Normal25 stdev
Normal100 mean
Normal100 stdev
Poisson25 mean
Poisson25 stdev
Poisson100 mean
Poisson100 stdev Lab #3 – Solution Total
Count
100
100
100
100
100
100
100
100 Mean
49.962
4.8757
50.012
5.0124
2.0428
1.4120
1.9917
1.4081 StDev
1.017
0.7121
0.507
0.3821
0.2959
0.2097
0.1397
0.1074 Page 5 of 5 ...
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This note was uploaded on 02/16/2010 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Staff
 Histograms

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