Question 1
In a study of typical student grade-point averages (GPAs), we sample 16 students and find an average GPA of 2.76, with a standard deviation of 0.48. Assuming the GPAs are normally distributed, what is an interval that we can be 80% certain contains the mean student GPA?
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(2.12, 3.40)
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(2.61, 2.91)
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(2.60, 2.92)
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(2.66, 2.86)
Question 2
In general, unbiased estimators are preferred for inference because:
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bias in inference is always bad and should be avoided at all costs, so using unbiased estimators is the only way to conduct objective inference.
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unbiased estimators always have the least amount of variance of all possible estimators.
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a biased estimator will almost always give very little insight into the parameter being estimated and, therefore, serves as a poor guess of the parameter’s true value.
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in many cases the most probable value of an unbiased estimator is the value of the parameter being estimated; thus, unbiased estimators typically converge on values near the parameter.
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