Question 207317: I have a population that I ran the mean for and got 55.1 as the Central measure of 10,000 data points.
Then I took 25 data points per sample and generated the sample means ( Actually ran 100 samples but I will sample the sample )
Here they are. Using Central Limit theorem concept, prove or disprove it by verifying the sample means approximate the population mean
to the ( at least ) 95% level of confidence
Sample means: 55.2, 55.7, 54.8, 54.9, 55.2, 55.3, 54.8, 55.1, 55.4, 54.6, 54.8, 55.2, 55.0, 54.9, 54.8, 55.0, 54.3
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I have a population that I ran the mean for and got 55.1 as the Central measure of 10,000 data points.
Then I took 25 data points per sample and generated the sample means ( Actually ran 100 samples but I will sample the sample )
Here they are. Using Central Limit theorem concept, prove or disprove it by verifying the sample means approximate the population mean
to the ( at least ) 95% level of confidence
Sample means: 55.2, 55.7, 54.8, 54.9, 55.2, 55.3, 54.8, 55.1, 55.4, 54.6, 54.8, 55.2, 55.0, 54.9, 54.8, 55.0, 54.3
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According to the CLT the mean of the sample means you have listed should
approach the mean of the population as the number of sample means increases,
and the standard deviation of the sample means should approach the quotient
of the population standard deviation and the sqrt(sample size) under the
same restriction.
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The mean of your sample means can be gotten by adding the sample means
you have listed and dividing by the number of sample means you have.
I get mean of sample means = 55 and standard deviation of the
sample means is 0.3260
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Ho: u(sample means) = 55.1
Ha: u(sample means) is not 55.1
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alpha = 5%
I ran a T-test and got the following:
test statistic: t = -1.2649..
p-value = 0.224...
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Conclusion: Since the p-value is greater than alpha=5%, Fail to
Reject Ho.
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Conclusion: The test results support the claim of the CLT
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Cheers,
Stan H.
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