9.1.3* When testing for an association between class level (Freshman, Sophomore, Junior, Senior) and IQ score, which of the following is NOT an appropriate way to write the alternative hypothesis?

A. There is an association between class level and IQ.

B. At least one of the population IQ means will be different.

C. Not all the population IQ means are the same.

D. FR

SO

JR

SR

9.1.4 Suppose you are comparing just two means. Among the possible statistics you could use is the difference in means, the MAD, or the max min (the difference between the largest mean and the smallest mean).

a. Will all three of these statistics always be the same? Will any pair of these statistics always be the same?

b. If one of the statistics is different from the other two, how is it related to them?

9.1.5* Suppose there is no association between class level (Fr, So, Jr, Sr) and the amount of sleep students get per night at a certain college. What does no association imply about the mean sleep hours for each class level?

9.1.6 Consider the following four boxplots constructed from the four data sets A, B, C, and D.

• Which data set has the largest interquartile range? Which has the smallest?
• Which data set has the largest median? Which has the smallest?
• Which data set looks like it could be skewed? In which direction could it be skewed?
• Which data set has the largest lower quartile?
• Which data set has the smallest sample size?

9.1.7* Consider the MAD statistic. What would happen if you did not take absolute values before calculating the sum of differences between group means? Why would this not be a useful calculation without taking absolute values?

9.1.8 For its numerator, the MAD statistic uses the sum of absolute pairwise differences. The absolute values get rid of possible negative differences. Instead of taking absolute values, what is another way to avoid summing negative differences?

9.1.9* Suppose three group means are 4, 5, and 10. Compute the value of the MAD statistic.

9.1.10 Suppose four group means are 2, 5, 7, and 8. Compute the value of the MAD statistic.

9.1.11 The plot shows total payroll in millions of dollars for the 30 major league teams of professional baseball sorted by league (National or American) and division (East, Central, West).

a. Identify the observational units, the response, and the explanatory variable.

b. For plots like the one above:

i. Each point represents a _______ (unit, response value,

value of the explanatory variable).

ii. Each horizontal cluster, taken as a whole, corresponds to a value of the _________ (response, explanatory) variable.

iii. Values along the horizontal axis represent values of the _________ (response, explanatory) variable.

C. The overall distribution of the response is (choose one):

A. Symmetric

B. Skewed right (a long tail points to the larger values)

C. Skewed left (a long tail points to the lower values)

D. No way to tell; need to see a histogram

d. Comparing groups by eye suggests that (choose one):

• Group means are roughly equal. A p-value will show weak evidence of differences between group means.
• Group means show substantial differences, but total payroll varies a lot within divisions. A p-value will not show strong evidence of group differences in means.
• Group means are roughly equal, but within-group variability is small enough that with several response values per group even the small differences in means will register as significant.
• Group means show substantial differences, and overall variability within divisions is small enough by comparison to differences in group means that a p-value will show evidence, possibly strong evidence, of differences.
• There is no way to tell without getting a computer to find the p-values.

9.1.23 A group of Hope College statistics students wanted to see if there was an association between students' major and the time (in seconds) it takes them to complete a small Sudoku-like puzzle. They grouped majors into four catego- ries: applied science (as), natural science (ns), social science (ss), and arts/humanities (ah). Their results can be found in the data file MajorPuzzle.

• Identify the explanatory variable and the response vari- able in this study.
• State, in words or symbols, the null and alternative hypotheses.
• Put the data in the Multiple Means applet and describe what the dotplots and means tell us about the association between major and time to complete the puzzle.
• What is the value of the MAD statistic?
• Use a simulation-based approach to determine if there is an association between a student's majors and the time it takes them to complete the puzzle. Be sure to report a p-value. Is there strong evidence of an association?

9.1.24 Reconsider Exercise 9.1.23 on major and time needed to complete a puzzle. There was one outlier in the applied science group. The researchers reported that this subject kept getting distracted while completing the puzzle. Suppose the first step in computing the MAD statistic was to find the differences in medians instead of the differences in means. How do you think this would change the value of the MAD statistic in this example? Explain.

9.1.25 Reconsider Exercise 9.1.23 on major and time needed to complete a puzzle. There was one outlier in the applied science group. The researchers reported that this subject kept getting distracted while completing the puz- zle. Put the data MajorPuzzle into the Multiple Means applet and run a simulation-based test using the MAD statistic.

• Remove the outlier (it should be at the top of the list) and run the test again. What is the new MAD statistic and p-value?
• After removing the outlier, you should have seen the MAD statistic decrease compared to the MAD statistics with the outlier in [see your answer to Exercise 9.1.23, part (d)]. Explain why this makes sense.
• After removing the outlier and getting a smaller MAD statistic, you might think that the p-value should increase. The p-value, however, decreased slightly compared to your answer to Exercise 9.1.23, part (e). What else changed that caused this to happen?