Estimation: Single Population

Which distribution is used to model the sampling distribution of sample variances?

• Normal distribution

• Student's t-distribution

• Chi-squared distribution

• F-distribution

As the sample size increases, the sampling distribution of sample variances approaches:

• A normal distribution

• A t-distribution

• A chi-squared distribution with degrees of freedom equal to the population size minus one

• A chi-squared distribution with degrees of freedom equal to the sample size minus one

The variance of the sampling distribution of sample variances is equal to:

• The population standard deviation squared divided by the sample size

• The population variance

• The sample standard deviation squared divided by the sample size

• The sample variance

The degrees of freedom for the sampling distribution of sample variances are equal to:

• The population size plus one

• The sample size minus one

• The sample size plus one

• The population size minus one

Which of the following is a desirable property of a point estimator?

• Unbiasedness

• Consistency

• Efficiency

• All of the above

A point estimator is said to be unbiased if:

• Its sampling distribution is centered around the true population parameter

• Its sampling distribution has a variance equal to the population parameter

• Its sampling distribution is normal

• Its sampling distribution is the same as the population distribution

The sample variance is a point estimator of the population variance. Which of the following is true about the bias of the sample variance estimator?

• It depends on the sample size

• It is always unbiased

• It is always biased

• It depends on the population distribution

Mean squared error (MSE) is a measure of:

• Bias of a point estimator

• Variance of a point estimator

• Both bias and variance of a point estimator

• None of the above

A point estimator has a bias of 2 and a variance of 5. What is the MSE of the estimator?

• 7

• 9

• 27

• 3