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Chapter 7: Q, 27 (page 457)

A statistic is an unbiased estimator of a parameter when

a. the statistic is calculated from a random sample.

b. in a single sample, the value of the statistic is equal to the value of the parameter.

c. in many samples, the values of the statistic are very close to the value of the

parameter.

d. in many samples, the values of the statistic are centered at the value of the parameter.

e. in many samples, the distribution of the statistic has a shape that is approximately

Normal.

Short Answer

Expert verified

The correct option is (d) in many samples, the values of the statistic are centered at the value of the parameter.

Step by step solution

01

 Step 1: Given information 

We have to find when a statistic is an unbiased parameter

02

Explanation for incorrect option(a)

The measurement is calculated from an irregular sample. That's not an imperative necessity in arrange to guarantee that measurement is unbiased.

03

Explanation for incorrect option(b)

In a single test, the esteem of the measurement is broken even with the esteem of the parameter. False, we require that in numerous tests the values of the measurement would be break even with the parameter

04

Explanation for incorrect option(c)

In numerous tests, the values of the measurement are exceptionally near to the esteem of the parameter. False, we require that in numerous tests the values of the measurement would be precisely break even with the parameter

05

Explanation for correct option(d)

In numerous tests, the values of the measurement are centered on the esteem of the parameter. True we have the two conditions fulfilled, centered at the parameter and the expected esteem is rise to the parameter.

Hence, (d) in many samples, the values of the statistic are centered at the value of the parameter is the correct answer.

06

Explanation for incorrect option(e)

In numerous tests, the dissemination of the measurement encompasses a shape that's around Normal. Not a select condition and not vital.

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