Relationship between Sample Size and Variability

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. What would happen to the sampling distribution of the sample median if the sample size were n = 50 instead? Justify

• It will be less variable because the sample size is larger.

• It will be more variable because the sample size is larger.

• It will be less variable because the sample size is smaller.

• It will be more variable because the sample size is smaller.

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. What would happen to the sampling distribution of the sample minimum if the sample size were n = 50 instead? Justify

• It will be more variable because the sample size is larger.

• It will be more variable because the sample size is smaller.

• It will be less variable because the sample size is larger.

• It will be less variable because the sample size is smaller.

To investigate if the sample range is an unbiased estimator of the population range of 153.73, 1000 SRSs of size n = 10 were selected from the population described. The sample range for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment. What would happen to the sampling distribution of the sample range if the sample size were n = 5 instead? Justify.

• It will be less variable because the sample size is smaller.

• It will be less variable because the sample size is larger.

• It will be more variable because the sample size is smaller.

• It will be more variable because the sample size is larger.

To investigate if the sample IQR is an unbiased estimator of the population IQR of 27.64, 1000 SRSs of size n = 10 were selected from the population described. The sample IQR for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment. What would happen to the sampling distribution of the sample IQR if the sample size were n = 5 instead? Justify.

• It will be more variable because the sample size is smaller.

• It will be more variable because the sample size is larger.

• It will be less variable because the sample size is smaller.

• It will be less variable because the sample size is larger.

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. What is the practical consequence of this change in sample size, n = 50?

• The estimated median amount spent will typically be closer to the true median amount spent. In other words, the estimate will be more precise.

• The estimated median amount spent will typically be farther away from the true median amount spent. In other words, the estimate will be more precise.

• The estimated median amount spent will typically be closer to the true median amount spent. In other words, the estimate will be less precise.

• The estimated median amount spent will typically be farther away from the true median amount spent. In other words, the estimate will be less precise.

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. What is the practical consequence of this change in sample size, n = 50?

• The estimated minimum amount spent will typically be closer to the true minimum amount spent. In other words, the estimate will be more precise.

• The estimated minimum amount spent will typically be closer to the true minimum amount spent. In other words, the estimate will be less precise.

• The estimated minimum amount spent will typically be farther away from the true minimum amount spent. In other words, the estimate will be more precise.

• The estimated minimum amount spent will typically be farther away from the true minimum amount spent. In other words, the estimate will be less precise.

To investigate if the sample range is an unbiased estimator of the population range of 153.73, 1000 SRSs of size n = 10 were selected from the population described. The sample range for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment. What is the practical consequence of this change in sample size, n = 5?

• The estimated range amount spent will typically be farther from the true range amount spent. In other words, the estimate will be less precise.

• The estimated range amount spent will typically be farther from the true range amount spent. In other words, the estimate will be more precise.

• The estimated range amount spent will typically be closer to the true range amount spent. In other words, the estimate will be less precise.

• The estimated range amount spent will typically be closer to the true range amount spent. In other words, the estimate will be more precise.

To investigate if the sample IQR is an unbiased estimator of the population IQR of 27.64, 1000 SRSs of size n = 10 were selected from the population described. The sample IQR for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment. What is the practical consequence of the change in sample size, n = 5?

• The estimated IQR amount spent will typically be farther from the true IQR amount spent. In other words, the estimate will be less precise.

• The estimated IQR amount spent will typically be farther from the true IQR amount spent. In other words, the estimate will be more precise.

• The estimated IQR amount spent will typically be closer to the true IQR amount spent. In other words, the estimate will be less precise.

• The estimated IQR amount spent will typically be closer to the true IQR amount spent. In other words, the estimate will be more precise.