Unbiased estimate for the population variance


Question: A random sample is taken from a population. The data points are: 5 4 9 2 1

a) What is the mode?

b) Calculate the unbiased estimate for the population variance.

c) Another random sample is taken from the population with an unbiased estimate of the population variance of 9.2. Does this result imply anything about whether the estimator is truly unbiased or not? Explain your answer.

d) A random sample of 92 observations is taken from another population. The sample mean is 5.5. The unbiased estimate for the population variance is 6.4. Test whether the population mean is equal to 3 or not at a significance level of 5%.

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Basic Statistics: Unbiased estimate for the population variance
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