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 1 year 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
53 59
13
59 46
14
59 ...
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a) If random samples of size 12 are drawn from a population with
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Assume that a population of size 5 specifies that all possible samples of size "3" are...
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Values:
2,500.00
2,650.00
2,790.00
3,125.00
3,200.00
1) Show that the expected value of the standard sampling error
is greater than the standard deviation of the population.
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a significance level of 80% and indicate which samples are not
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3) Select the non-representative samples and calculate the
mean...
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
samples of size "3" are extracted without repetition.
Values:
2,500.00
2,650.00
2,790.00
3,125.00
3,200.00
1. Show that the expected value of the standard sampling error
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with a confidence level of 84% and develop an analysis.
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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P(p̂ > 0.78) =
Random samples of size n = 60 were selected from a binomial population with p =...
Random samples of size n = 60 were selected from a
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(a)
P(p̂ ≤ 0.22) =
(b)
P(0.18 ≤ p̂ ≤ 0.22) =
Use the population {3,4,6} and assume that samples of size 2 are randomly selected, with replacement....
Use the population {3,4,6} and assume that samples of size 2 are
randomly selected, with replacement.
?) 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 the population {3,4,6} and assume that samples of size 2 are randomly selected, with replacement....
use
the population {3,4,6} and assume that samples of size 2 are
randomly selected, with replacement. a) for the population, find
the proportion of odd numbers. b) construct a table for sampling
distribution of the sample proportion of odd numbers. c) find the
mean of sampling distribution of the sample proportion of odd
numbers. d) is the sample proportion and unbiased estmator or.
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A random sample of size n = 69 is taken from a population of size N...
A random sample of size n = 69 is taken from a
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a-1. Is it necessary to apply the finite
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a-2. Calculate the expected value and the
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Expected Value-
Standard Error-
b. What is the probability that the sample
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