A biologist is studying the effects that applying insecticide to a fruit farm has on the local bat population. She collects 23 bats and finds the mean weight of this sample to be 503.4 grams. Assuming the selected bats are a random sample, she concludes that because the sample mean is an unbiased estimator of the population mean, the mean weight of bats in the population is also 503.4 grams. Explain why this is an incorrect interpretation of an unbiased estimator.

A. Having an unbiased estimator means that the mean of the means of all possible samples of the same size would be the same as the population mean.

B. having an unbiased estimator means that the sample mean will not be equal to the population mean.

C. having an unbiased estimator means that at least two sample means are the same as the population mean.

D. having an unbiased estimator means that none of the sample means will be equal to the population mean.

Question

Marley Payne

Mathematics

10 August, 07:57

A biologist is studying the effects that applying insecticide to a fruit farm has on the local bat population. She collects 23 bats and finds the mean weight of this sample to be 503.4 grams. Assuming the selected bats are a random sample, she concludes that because the sample mean is an unbiased estimator of the population mean, the mean weight of bats in the population is also 503.4 grams. Explain why this is an incorrect interpretation of an unbiased estimator.

A. Having an unbiased estimator means that the mean of the means of all possible samples of the same size would be the same as the population mean.

B. having an unbiased estimator means that the sample mean will not be equal to the population mean.

C. having an unbiased estimator means that at least two sample means are the same as the population mean.

D. having an unbiased estimator means that none of the sample means will be equal to the population mean.

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Answers (1)

Know the Answer?

Teresa Nielsen · Answer 1

Answer: the correct answer is A. Having an unbiased estimator means that the mean of the means of all possible samples of the same size would be the same as the population mean.

Step-by-step explanation:

The problem is that is just one sample of 23 bats so the experiment is very limited to say that the population mean is 503.4 since an unbiased estimator is in more mathematical terms if the estimator (i. e. the sample mean) equals the parameter (i. e. the population mean), then it's an unbiased estimator.