Chapter 7.1, Problem 19E

(a)

To determine

The statistics which are unbiased estimators.

Answer to Problem 19E

The graphs (b) and graph (c) are unbiased estimators.

Explanation of Solution

Given information:

The histograms:

  

  

  

  

If the mean and the value of a statistic are equal, then the statistic becomes and unbiased estimator.

In the graphs (b) and (c), it is seen that the mean and the population parameter falls together which means the graph (b) and graph (c) are unbiased estimator.

Hence, the graphs (b) and graph (c) are unbiased estimators.

(b)

To determine

The statistic which does the best job of estimating the parameter.

Answer to Problem 19E

The graph (b) does the best job of estimating the parameter.

Explanation of Solution

Given information:

The histograms:

  

  

  

  

The graph which has the its bars centered about the population parameter without any gaps between the bars does the best job of estimating the parameter. Also, in a graph if there exist gaps between the bars then it is less likely estimate the accurate values.

In the graph (b), there are no gaps between the bars and the bars are centered about the population parameter.

Hence, the graph (b) does the best job of estimating the parameter.