Consider a small population of N = 5 units, labeled 1, 2, 3, 4, 5, with respecti
ID: 3200939 • Letter: C
Question
Consider a small population of N = 5 units, labeled 1, 2, 3, 4, 5, with respective y-values 3, 1, 0, 1, 5. Consider a simple random sampling design with a sample size n = 3. For your convenience, several parts of the following may be combined into a single table. (a) Give the values of the population parameters mu, tau, and sigma^2. List every possible sample of size n = 3. For each sample, what is the probability that it is the one selected? (b) For each sample, compute the sample mean y and the sample median m. Demonstrate that the sample mean is unbiased for the population mean and determine whether the sample median is unbiased for the population median.Explanation / Answer
Answer:
a).
Descriptive statistics
data
N
5
Population mean
2.00
population variance
3.20
population standard deviation
1.79
Population median
1.00
y1,y2,y3,y4 and y5 are items.
S1, S2 and S3 are items in each samples.
S1
S2
S3
3
1
0
3
1
1
3
1
5
3
0
1
3
0
5
3
1
5
1
0
1
1
0
5
1
1
5
0
1
5
Probability of each sample = 1/10 = 0.1
b).
S1
S2
S3
Mean
Median
3
1
0
1.3333
1
3
1
1
1.6667
1
3
1
5
3.0000
3
3
0
1
1.3333
1
3
0
5
2.6667
3
3
1
5
3.0000
3
1
0
1
0.6667
1
1
0
5
2.0000
1
1
1
5
2.3333
1
0
1
5
2.0000
1
Mean=2.0000
Median =1
Mean of sample means = 2 is same as population mean 2.
Sample mean is unbiased for the population mean.
Median of sample medians = 1 is same as population median 1.
In this case, Sample median is unbiased for the population median.
Descriptive statistics
data
N
5
Population mean
2.00
population variance
3.20
population standard deviation
1.79
Population median
1.00