The Illinois State Board of Education conducts an annual study of the salaries of Illinois teachers. The study looks at how teachers' salaries are distributed based on factors such as degree and experience level, district size, and geographic region.

The table shows the beginning salaries of a random sample of Illinois teachers from different-sized districts. District size is measured by the number of students enrolled.

In Exercises 1-3, refer to the samples listed below. Use \(\alpha=0.05\).

(a) Under 500 students

(b) 1000-2999 students

(c) At least 12,000 students 1. Are the samples independent of each other? Explain.

2. Use technology to determine whether each sample is from a normal, or approximately normal, population.

3. Use technology to determine whether the samples were selected from populations having equal variances.

4. Using the results of Exercises 1-3, discuss whether the three conditions for a one-way ANOVA test are satisfied. If so, use technology to test the claim that teachers from districts of the three sizes have the same mean salary. Use \(\alpha=0.05\).

5. Repeat Exercises 1-4 using the data in the table below. The table displays the beginning salaries of a random sample of Illinois teachers from different geographic regions of Illinois.

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Teacher salaries Under At least 500 1000-2999 12,000 students students students 36,462 41,862 40,726 40,877 40,482 39,640 33,937 38,292 40.686 32,957 38,264 37,347 38,313 43.385 46,239 30,313 36.195 44.064 33,490 44,117 41,855 41,357 31.188 39,476 29,892 38,746 44,136 35,237 32,760 44,966 29,760 41,527 46,992 36,580 40,814 39,257 33,547 29,997 39,572