Question

In: Statistics and Probability

Select True or False, depending on whether the corresponding statement is true or false. 1. An...

Select True or False, depending on whether the corresponding statement is true or false.

1. An unbiased estimator is a sample statistic that has a mean (or expected value) equal to the value of the population parameter.

2. In order to construct a confidence interval estimate of the population mean, the value of the population mean is needed.

3. The larger the level of confidence used in constructing a confidence interval estimate of the population mean, the narrower the confidence interval.

4. The confidence level of a confidence interval gives the probability that such an interval selected at random will contain the population parameter.

5. Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

Solutions

Expert Solution

1.

An unbiased estimator is a sample statistic that has a mean (or expected value) equal to the value of the population parameter.

Correct option:

True

Explanation:

A statistic is unbiased if the mean of the sampling distribution of the statistic is equal to the parameter.

2.

In order to construct a confidence interval estimate of the population mean, the value of the population mean is needed.

Correct option:

False

Explanation:
Confidence interval for population mean is given by:

,

so population mean is not required for calculating Confidence interval for population mean .

3.

The larger the level of confidence used in constructing a confidence interval estimate of the population mean, the narrower the confidence interval.

Correct option:

False

Explanation:

The width of the confidence interval increases as the confidence level increases.

4.

The confidence level of a confidence interval gives the probability that such an interval selected at random will contain the population parameter.

Correct option:

True'

Explanation:
The confidence interval is a range of values we are confidence level percent certain will contain population parameter.

5.

Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

Correct option:

True

Explanation:

An unbiased estimator is a sample statistic that has a mean (or expected value) equal to the value of the population parameter. So, closeness of the estimator is to the parameter is not known.

orchestra answered 1 year ago
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