Bias and Unbiased Estimators for Sampling Distributions

A z-score tells you...

• the standard deviation of a sampling distribution.
• the original raw score on which it is based.
• if the distribution it comes from is normal.
• how many standard deviations away from the mean a score lies.

Increasing the sample size of an opinion poll will reduce the

• bias of the estimates made from the data collected in the poll.
• variability of the estimates made from the data collected in the poll.
• variability of opinions in the sample.
• variability of opinions in the population.

A statistic is an unbiased estimator of a parameter when

• the statistic is calculated from a random sample.
• in many samples, the values of the statistic are very close to the value of the parameter.
•  in a single sample, the value of the statistic is equal to the value of the parameter
• in many samples, the values of the statistic are centered at the value of the parameter.

Find the area under the standard normal curve to the right of z = -2.67.

• 0.0869
• 0.9962
• 0.0008
• 0.1234

Find the area under the standard normal curve to the right of z = 3.15. 

• 0.0869
• 0.9962
• 0.0008
• 0.1234

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population
• The Sample
• The Sampling Distribution

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population
• The Sample
• The Sampling Distribution

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population
• The Sample
• The Sampling Distribution

To investigate if the sample median is an unbiased estimator of the population median of 22.96, 1000 SRSs of size n = 10 were selected from the population described. The sample median for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment. Does the sample median appear to be an unbiased estimator of the population median? Explain your reasoning.

• Yes, the mean of the sampling distribution is very close to 22.96, the value of the population median.

• Yes, the mean of the sampling distribution is very far from 22.96, the value of the population median.

• No, the mean of the sampling distribution is not very close to 22.96, the value of the population median.

• No, the mean of the sampling distribution is not very far from 22.96, the value of the population median.

To investigate if the sample minimum is an unbiased estimator of the population minimum of 0.20, 1000 SRSs of size n = 10 were selected from the population described. The sample minimum for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment. Does the sample minimum appear to be an unbiased estimator of the population minimum? Explain your reasoning.

• Yes, the mean of the sampling distribution is very close to 0.20, the value of the population minimum.

• Yes, the mean of the sampling distribution is clearly more than 0.20, the value of the population minimum.

• No, the mean of the sampling distribution is clearly more than 0.20, the value of the population minimum.

• No, the mean of the sampling distribution is very close to 0.20, the value of the population minimum.