Econometrics Exam 1

Which of the following is a characteristic for a good estimator? a. All of these choices are true. b. Being consistent c. Being unbiased d. Having relative efficiency

a. All of these choices are true.

Which of the following would be an appropriate alternative hypothesis? a. The mean of a population is greater than 70. b. The mean of a sample is equal to 70. c. The mean of a population is equal to 70. d. The mean of a sample is greater than 70.

a. The mean of a population is greater than 70.

A point estimator is defined as: a. a single value that estimates an unknown population parameter. b. a single value that estimates an unknown sample statistic. c. a range of values that estimates an unknown sample statistic. d. a range of values that estimates an unknown population parameter.

a. a single value that estimates an unknown population parameter.

An unbiased estimator of a population parameter is defined as: a. an estimator whose expected value is equal to the true parameter. b. an estimator whose variance is equal to one. c. an estimator whose variance goes to zero as the sample size goes to infinity. d. an estimator whose expected value is equal to zero.

a. an estimator whose expected value is equal to the true parameter.

The probability of a Type II error is denoted by: a. b b. 1 - b c. 1 - a d. a

a. b

If we reject the null hypothesis when it is false, then we have committed: a. neither a Type I error nor a Type II error. b. a Type II error. c. a Type I error. d. both a Type I error and a Type II error.

a. neither a Type I error nor a Type II error.

We cannot commit a Type I error when the: a. null hypothesis is false. b. level of significance is 0.10. c. null hypothesis is true. d. test is a two-tail test.

a. null hypothesis is false.

If there are two unbiased estimators of a population parameter available, the one that has the smallest variance is said to be: a. relatively efficient. b. a biased estimator. c. consistent. d. relatively unbiased.

a. relatively efficient.

Sampling distributions describe the distributions of: a. sample statistics. b. None of these choices. c. both parameters and statistics d. population parameters.

a. sample statistics.

Which of the following probabilities is equal to the significance level a? a. Probability of rejecting H0 when you are supposed to. b. Probability of making a Type I error. c. Probability of making a Type II error. d. Probability of not rejecting H0 when you shouldn't.

b. Probability of making a Type I error.

A sample of size n is selected at random from an infinite population. As n increases, which of the following statements is true? a. The standard error of the sample mean increases. b. The standard error of the sample mean decreases. c. The population standard deviation decreases. d. The population standard deviation increases.

b. The standard error of the sample mean decreases.

A Type II error is committed if we make: a. a correct decision when the null hypothesis is true. b. an incorrect decision when the null hypothesis is false. c. a correct decision when the null hypothesis is false. d. an incorrect decision when the null hypothesis is true.

b. an incorrect decision when the null hypothesis is false.

In a criminal trial, a Type I error is made when: a. a guilty defendant is acquitted. b. an innocent person is convicted. c. a guilty defendant is convicted. d. an innocent person is acquitted.

b. an innocent person is convicted.

If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean will be: a. approximately normal for all values of n. b. exactly normal for all values of n. c. approximately normal only for large n (n > 30). d. exactly normal only for large n (n > 30).

b. exactly normal for all values of n.

In a criminal trial, a Type II error is made when: a. an innocent person is acquitted. b. an innocent person is convicted. c. a guilty defendant is acquitted. d. a guilty defendant is convicted.

c. a guilty defendant is acquitted.

A Type I error is committed if we make: a. a correct decision when the null hypothesis is false. b. a correct decision when the null hypothesis is true. c. an incorrect decision when the null hypothesis is true. d. an incorrect decision when the null hypothesis is false.

c. an incorrect decision when the null hypothesis is true.

The Central Limit Theorem states that, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean : a. None of these choices. b. is approximately normal if n is small (n < 30). c. is approximately normal if n is large (n > 30). d. is approximately normal if the underlying population is normal.

c. is approximately normal if n is large (n > 30).

A Type I error occurs when we: a. don't reject a true null hypothesis. b. reject a false null hypothesis. c. reject a true null hypothesis. d. don't reject a false null hypothesis.

c. reject a true null hypothesis.

Which of the following is true regarding the sampling distribution of the mean for a large sample size? Assume the population distribution is not normal. a. It the same mean and standard deviation as the population, but a different shape. b. It has the same shape and mean as the population, but a different standard deviation. c. It has the same shape, mean and standard deviation as the population. d. It has the same mean as the population, but a different shape and standard deviation.

d. It has the same mean as the population, but a different shape and standard deviation.

Which of the following is an appropriate null hypothesis? a. All of these choices are true. b. The mean of a sample is equal to 60. c. The mean of a population is not equal to 60. d. The mean of a population is equal to 60.

d. The mean of a population is equal to 60.

Suppose the ages of students in your program follow a positively skewed distribution with mean of 24 years and a standard deviation of 4 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is NOT true? a. The shape of the sampling distribution of sample mean is approximately normal. b. All of these choices are true. c. The mean of the sampling distribution of sample mean is equal to 24 years. d. The standard deviation of the sampling distribution of sample mean is equal to 4 years.

d. The standard deviation of the sampling distribution of sample mean is equal to 4 years.

Suppose X has a distribution that is not normal. The Central Limit Theorem is important in this case because: a. it says the sampling distribution of X-bar is exactly normal, for any sample size. b. it says the sampling distribution of X-bar is approximately normal for any sample size. c. None of these choices. d. it says the sampling distribution of X-bar is approximately normal if n is large enough.

d. it says the sampling distribution of X-bar is approximately normal if n is large enough.

The standard deviation of the sampling distribution of X-bar is also called the: a. population standard deviation. b. finite population correction factor. c. central limit theorem. d. standard error of the sample mean.

d. standard error of the sample mean.

An estimator is said to be consistent if: a. it is an unbiased estimator. b. the variance of the estimator is zero. c. the difference between the estimator and the population parameter stays the same as the sample size grows larger. d. the difference between the estimator and the population parameter grows smaller as the sample size grows larger.

d. the difference between the estimator and the population parameter grows smaller as the sample size grows larger.