Question
In: Statistics and Probability
7. Use the population of {1, 3, 7}. Assume that the random samples of size n...
7. Use the population of {1, 3, 7}. Assume that the random samples of size n = 2 Construct a sampling distribution of the sample mean. After identifying the 9 different possible samples (with replacement), find the mean of each sample, then construct a table representing the sample the sampling distribution of the sample mean. In the table, combine values of the sample mean that are the same. (Hint: condense the table similar to examples presented in class.)
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Solutions
Expert Solution
We have the population {1,3,7}.
Let x1, x2, ..., xn be a random sample of size n.
Then the sample mean is given by the formula
.
Here, since we are taking sample of size 2, say x1 and x2, the sample mean can be obtained as
case (i): Random sample of size 2 with replacement.
The following are the possible samples with their corresponding sample means.
| Samples (with replacement) |
Sample means |
| {1,1} | 1 |
| {1,3} | 2 |
| {1,7} | 4 |
| {3,1} | 2 |
| {3,3} | 3 |
| {3,7} | 5 |
| {7,1} | 4 |
| {7,3} | 5 |
| {7,7} | 7 |
Therefore the sampling distribution of sample mean is obtained as in the following table.
 |
 |
| 1 | 1/9 |
| 2 | 2/9 |
| 3 | 1/9 |
| 4 | 2/9 |
| 5 | 2/9 |
| 7 | 1/9 |
case (ii): Random sample of size 2 without replacement. (mentioned additionally, not asked in the question)
The following are the possible samples with their corresponding sample means.
| Samples (without replacement) |
Sample means |
| {1,3} | 2 |
| {1,7} | 4 |
| {3,7} | 5 |
Therefore the sampling distribution of sample mean is obtained as in the following table.
|
|
| 2 | 1/3 |
| 4 | 1/3 |
| 5 | 1/3 |
orchestra answered 3 years agoRelated Solutions
7. Assume a population of 46, 51, 53, and 59. Assume that samples of size n=2...
7. Assume a population of 46, 51, 53, and 59. Assume that
samples of size n=2 are randomly selected with replacement from the
population. Listed below are the sixteen different samples.
Complete parts
(a) through (c).
Sample x1 x2
1
46 46
2
46 51
3
46 53
4
46 59
5
51 46
6
51 51
7
51 53
8
51 59
9
53 46
10
53 51
11
53 53
12
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13
59 46
14
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2,790.00
3,125.00
3,200.00
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Assume that a population of size 5 specifies that all possible samples of size "3" are...
Assume that a population of size 5 specifies that all possible
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Values:
2,500.00
2,650.00
2,790.00
3,125.00
3,200.00
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Random samples of size n = 330 are taken from a
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(Round the value for the centerline to 2 decimal places and
the values for the UCL and LCL to 3 decimal places.)
Centerline _________
Upper control limit __________
Lower control limit __________
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Random samples of size n = 90 were selected from a binomial population with p =...
Random samples of size n = 90 were selected from a
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Random samples of size n = 60 were selected from a binomial population with p =...
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(a)
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(b)
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Use the population {3,4,6} and assume that samples of size 2 are
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?) For the population, find the proportion of odd numbers
?) Construct a table for the sampling distribution of the sample
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?) Find the mean of the sampling distribution of the sample
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?) Is the sample proportion an unbiased estimator or a biased
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use
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