A company provides tuition for mathematics students across the country. It provides two levels of tuition: tuition for general-level students and tuition for advanced-level students. All students who receive tuition at this company must assess their initial comprehension of mathematics.

For general-level students, the population mean score in this test is 50.13, with a population standard deviation of 14.28. For advanced students, the population mean score in the test is 80.22, with a population standard deviation of 11.03.

A statistician wants to study the results of a random selection of general students and a random selection of advanced students. The statistician intends to draw a sample of 200 general-level students and a sample of 50 advanced-level students.

a)From the following list, select the statements that are true. For each statement, assume that all other measures remain constant in that instance.

The larger a population mean, the greater the variation in sample means for samples from that population.

The smaller a population mean, the greater the variation in sample means for samples from that population.

The larger a population variance, the greater the variation in sample means for samples from that population.

The smaller a population variance, the greater the variation in sample means for samples from that population.

The larger the sample size for samples from a population, the greater the variation in sample means.

The smaller the sample size for samples from a population, the greater the variation in sample means.

b)For the samples described in the scenario above, the sample mean scores for samples of general-level students will have a

higher or lower

level of variation than the variation in sample mean scores for samples of advanced-level students.