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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

The student newspaper at a large university asks an SRS of 250undergraduates, 鈥淒o you favor eliminating the carnival from the term-end celebration?鈥� All in all, 150of the 250are in favor. Suppose that (unknown to you) 55%of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n=250from this population, the sampling distribution of the sample proportion P鈭�would be

(a) exactly Normal with mean 0.55and standard deviation of 0.03

(b) approximately Normal with mean 0.55and standard deviation 0.03.

(c) exactly Normal with mean 0.60and standard deviation 0.03.

(d) approximately Normal with mean 0.60and standard deviation 0.03.

(e) heavily skewed with mean 0.55and standard deviation 0.03.

Cold cabin? The Fathom screenshot below shows the results of taking 500SRSs of 10temperature readings from a population distribution that鈥檚 N(50,3)and recording the sample minimum each time.

(a) Describe the approximate sampling distribution.

(b) Suppose that the minimum of an actual sample is 40掳F. What would you conclude about the thermostat manufacturer鈥檚 claim? Explain.

A researcher initially plans to take anSRS of size n from a population that has a mean of 80 and a standard deviation of 20. If he were to double his sample size (to 2n), the standard deviation of the sampling distribution of the sample mean would be multiplied by

(a) 2.

(b)12 .

(c) 2.

(d) 12.

(e)12n

In the language of government statistics, you are 鈥渋n the labor force鈥� if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Here are data from the Current Population Survey for the civilian population aged 25years and over in a recent year. The table entries are counted by thousands of people.

Unemployment (5.1) What is the probability that a randomly chosen person 25 years of age or older is in the labor force? Show your work.

The name for the pattern of values that a statistic takes when we sample repeatedly from the same population is

(a) the bias of the statistic.

(b) the variability of the statistic.

(c) the population distribution.

(d) the distribution of sample data.

(e) the sampling distribution of the statistic.
See all solutions

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