Question 1077656: The data in the table represent the ages of the winners of an award for the past five years. Use the data to answer questions (a) through (e).
Data table: 61 36
31 31
50
a) compute the population mean
b)compute the mean for all 5C2=10 samples with a sample size of 2
c)Construct a sampling distribution for the mean by listing the sample mean and their corresponding probabilities.
d) compute the mean of the sampling distribution
Is anyone able to help and answer any of this? I'm so stuck on this problem, thank you!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The mean of the population is 209/5=41.8
The mean of all samples of n=2 will be:
48.5
46
55.5
46
33.5
31
40.5
43
40.5
33.5
sum is 418, and mean is 41.8, same as the population mean.
Each one of the 10 samples will be a point estimate of the sample mean.
31 (0.1 probability)-3.1
33.5 (0.2)----------6.7
40.5 (0.2)----------8.1
43 (0.1)------------4.3
46 (0.2)------------9.2
48.5 (0.1)----------4.85
55.5 (0.1)----------5.55
That sum is 41.8
Not required but the standard deviation of the original population is 11.855
The sd of the 10 samples is 7.26. This turns out to be 11.855/sqrt(2), and this is a basic property of the sampling distribution from a population. It will have the same mean as the population, and its sd is sd of pop, or
sigma/sqrt(n), the sample size. This is one of the most important concepts in statistics.
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