Question

Answer these questions:

1. Under what real-world conditions might a biased but efficient sample be preferable to an unbiased but inefficient one?

2. You have obtained a “good” sample (adequate size, normality assumption justified, no skewness, no problems with outliers). So you calculate the z statistic, and Z = 0.03. Without reference to the statistical tables or a software package, what is your immediate conclusion about the sample with respect to the underlying population?

3. In estimating the variance in a sample proportion p, it is most conservative to assume that the true underlying population proportion pi is 50% (π = .5). Why? Hint: examine the equation, and think through why 50% produces a most conservative estimate.

4. Null hypotheses are most properly said to be either “rejected,” or “fail to be rejected.” That seems odd—why don’t we just say, “rejected” or “accepted?”

5. In hypothesis testing, we must select either a “one-tailed” test or a “two-tailed” test. Consider a road trip across a vast uninhabited desert in an automobile—beforehand, you are going to sample the gas mileage your automobile achieves, and use that to estimate the amount of gas you’ll need to cross the desert. Will you use a one-tailed test or a two-tailed test, and why?

Solution Preview

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1. The Root Mean Squared Error (RMSE) of the sample would be used since it measures biasness as well as efficiency and is a better assessor of the performance of the sample. If this error is low for biased but efficient sample, the same would be preferred. The important thing about the sample is that it should be consistent...

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