STAT 350 – Fall 2008
Lab #2 – SOLUTION
1.
Give the sidebyside histograms for
,25
N
x
and
,100
N
x
.
53
52
51
50
49
48
40
30
20
10
0
53
52
51
50
49
48
Normal25 mean
Frequency
Normal100 mean
Histogram of Normal25 mean, Normal100 mean
(i)
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.
(ii)
What is the shape of each distribution?
Each distribution is approximately symmetric and bellshaped
(iii)
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.
(iv)
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.
(v)
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
answers should be close to
5
n
(1 and 0.5).
For the data graphed above, the standard
deviations were 1.017 and 0.508 respectively.
(iv)
Does the standard deviation appear to be affected by increasing the sample size.
If
so, how?
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 Fall '08
 Staff
 Histograms, Standard Deviation

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