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Chapter 7: Q.3.1 (page 426)

The histogram above left shows the intervals (in minutes) between eruptions of the Old Faithful geyser for all 222recorded eruptions during a particular month. For this population, the median is 75minutes. We used Fathom software to take 500SRSs of size 10from the population. The 500values of the sample median are displayed in the histogram above right. The mean of the 500sample median values is 73.5.

Is the sample median an unbiased estimator of the population median? Justify your answer

Short Answer

Expert verified

The sample median is an unbiased estimator of the population median.

Step by step solution

01

Given Information

Median is75.

Sample size is500

Mean is73.5

02

Explanation

From the given information, it is clear that the mean of the distribution and the sample median are not equal. Thus, it cannot be said that the sample median is an unbiased estimator of the population median.

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Most popular questions from this chapter

Run a mile During World War II, able-bodied male undergraduates at the University of Illinois participated in required physical training. Each student ran a timed mile. Their times followed the Normal distribution with mean 7.11minutes and standard deviation 0.74minute. An SRS of 100of these students has mean time x¯=7.15minutes. A second SRS of size100has mean x¯=6.97minutes. After many SRSs, the values of the sample mean x follow the Normal distribution with mean 7.11 minutes and standard deviation0.074minute.

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