1. Consider the average pupil/teacher ratio (3rd column) in the data set. Run the
   explore command in SPSS and interpret as much of the output as possible from the box:
   mean, trimmed mean, std. dev. kurtosis, etc.
2. Consider the SAT and spending data: is there a correlation between the pupil/teacher ratio and the verbal SAT scores? What does the scatter plot look like? Is the correlation
   significant? For every decrease of 5 students per teacher, what is the corresponding change in the verbal SAT scores? Should the class sizes be larger or smaller? Explain why this relationship may exist.
3. Consider the SAT and spending data: Is there a correlation between the average annual salary of teachers in public elementary schools and secondary schools and the average math SAT scores? What does the scatterplot look like? Is the correlation significant?
   for every increase of 1,000 dollars in teacher pay, what is the corresponding
   change in the math SAT score? If a state spends 40,000 dollars per year, on average, per teacher, what math SAT score should they expect? Should teachers receive more or less pay to improve math SAT scores? explain why this relationship may exist.
   Give an appropriate interpretation of the r ² value.
   For the next questions: Let us consider the state spending on education and SAT scores data set. Let's truncate the data, so that we have a sample, not a population. Consider only the state data (in alphabetical order) down to Kansas. Temporarily delete the other data. there should be 16 states remaining.
4. What is a 95% confidence interval for the mean of teacher salaries? Based on this interval, what is a logical and valid conclusion regarding the population mean of teacher salaries? Why is it not valid to do this on the entire data set? (consider if this was a sample or not)

For the next three questions, you must answer the following seven points:

1. Is this a one or two tailed test?
2. State the null hypothesis
3. State the alternative hypothesis
4. calculate the z-score
5. what is the critical value
6. what is the conclusion
7. what does it all mean? In other words, interpret the conclusion in light of the data and the overall situation

5. Test the hypothesis that mean state spending per pupil is greater than 5,000 dollars.

6. Test the hypothesis that SAT verbal scores are different than SAT math scores.

7. Test the hypothesis that SAT verbal scores are at least 50 points greater than SAT math scores.

8. When is it advisable to use a trimmed mean to describe the average of a data set?

9. Use the ISAT data set to make a box and whisker plot. Explain the test for outliers and if there are any, identify them correctly.

10. Why is it important to look at a scatterplot before doing any linear regression?

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