MATCHING: For the following problems, write the letter of ...



MATCHING: For the following problems, write the letter of the most appropriate statistical analysis technique next to the story. Note: each answer choice may be used once, more than once, or not at all.

|A. Mean and/or standard |B. Simple linear regression |C. Multiple linear |D. 1-sample mean t-test |

|deviation | |regression | |

|E. Matched pairs t-test |F. Comparison of means |G. 1-sample proportion |H. 2-sample proportion Z-test |

| |t-test |Z-test | |

|I. Chi-squared test |J. One-way ANOVA |K. Two-way ANOVA |L. Five number summary |

1. Is college major associated with the region of the country a student is from in the population?

2. A group of taste testers is asked to rate (in random order) both Coke and Pepsi on a scale of 1-10. Is Coke better tasting than Pepsi on average in the population?

3. What is the average taste test rating for Coke on a scale of 1-10 from a sample of 30 taste testers?

4. Do major and region of the country a student is from affect the population mean GPA?

5. Which of the following are important for predicting a student’s graduation GPA in the population: the number of semesters a student spends in college, their high school GPA, and their SAT scores?

6. Is the population percentage of people in Tippecanoe county who are Purdue students significantly higher in 2007 than it was in 1994 if a random sample of residents was taken both years?

7. Are height and weight independent in the population?

8. Are freshman taller than seniors on average in the population?

9. Are population average GPAs the same for science and engineering majors?

10. Are population average GPAs the same for science, engineering, nursing, and communications majors?

11. Is the population average GPA 3.0?

12. What is the middle GPA for this sample of students?

MATCHING: (3 points each) For problems 1-11, write the letter of the most appropriate statistical analysis technique next to the story.

Note: each answer choice may be used once, more than once, or not at all.

| |Mean and/or standard deviation |

|Does knowing a college student’s SAT score tell us anything about his or her first year college GPA in the |Five number summary |

|population? |Simple linear regression |

| |Multiple linear regression |

|Do college grade point averages differ for male athletes in football, swimming, and crew in the population? |1-sample mean t-test |

| |Matched pairs t-test |

|A college instructor wants to know whether the population average high school GPA for freshman enrolled in |2-sample (Comparison of means) t-test |

|college algebra is below 3.0. |1-sample proportion Z-test |

| |2-sample proportion Z-test |

|Does knowing high school seniors’ IQ scores, SAT scores, and high school GPA tell us anything about their first |Chi-squared test |

|year college GPAs in the population? |One-way ANOVA |

| |Two-way ANOVA |

|Do New Mexican high school seniors have higher population averages than Vermont high school seniors on the | |

|national achievement exam? | |

| | |

|Is college major related to political party affiliation in the population? | |

| | |

|Do identical twins differ from each other on average in reading achievement scores in the population? | |

| | |

|Is support for a school bond issue (Yes or No) higher in the University Farms than in Chauncey Village | |

|neighborhoods? | |

| | |

|Is there a difference in population average national achievement exam scores for seniors from New Mexico, | |

|Florida, and Vermont? | |

| | |

|What is the average national achievement exam score for 200 New Mexico high school seniors? | |

| | |

|Do college major and gender affect the mean GPA for the population of Purdue students? | |

|A. Mean and/or standard |B. Simple linear regression |C. Multiple linear regression |D. 1-sample mean t-test |

|deviation | | | |

|E. Matched pairs t-test |F. Comparison of |G. 1-sample |H. 2-sample proportion |

| |means t-test |proportion Z-test |Z-test |

|I. Chi-squared test |J. One-way ANOVA |K. Two-way ANOVA |L. Five number summary |

1. What is the average amount of money students in this class spend each year on vacations?

2. Do more than 75% of college students in the population go someplace other than to their parents’ house for spring break?

3. Does the amount of debt a student has increase, on average in the population, if you compare before and after spring break credit card statements?

4. Are g.p.a. and amount of credit card debt independent in the population?

5. Is there a difference in average amount of credit card debt if you compare freshman, sophomores, juniors and seniors in the population of college students?

6. What is the range of the middle 50% of my 50 students’ exam scores?

7. Is there a relationship between the number of students enrolled in a class and the average exam score for that class for all the classes at Purdue?

8. Do Indiana-born students score higher on average in the population on this test than students born outside the state?

9. Is the population mean of all students taking a national exam different from the 80 that the authors aimed for?

10. Are political party preference (Democrat, Republican, and Independent) and ice cream flavor preference related in the population?

11. Is the population percentage of unemployed men lower than for unemployed women?

12. Are the type of pet you own and your hair color related to your annual salary in the population?

13. Is there a population mean difference in preschoolers’ spatial-temporal reasoning scores after having piano lessons?

14. Do higher I.Q. people also have higher college g.p.a.s in the population?

15. Do annual salary, I.Q., and number of children affect a person’s happiness rating (on a scale of 1-10) in the population?

16. Do flavor of M&Ms (plain, peanut, and peanut butter) and color distribution (red, orange, yellow, green, blue, and brown) make a difference to the population mean taste ratings (scale of 1-10)?

17. Is there a difference in the population average number of chips in a regular Chips Ahoy cookie and a reduced-fat cookie?

18. Is the type of music playing over the speakers in a store associated with the type of wine a customer buys in the population?

19. What is the average number of calories in a sample of 20 “fun packs” of Halloweeen candy?

20. Does the season (fall, winter, spring, summer) make a difference to population average pollen counts?

21. Does the season (fall, winter, spring, summer) and type of trees growing nearby make a difference to population average pollen counts?

22. Do the temperature (in degrees), number of trees growing nearby, and % humidity affect pollen counts in the population?

23. Do pollen counts decrease on average between noon and midnight on particular days if a sample of 30 days is used to estimate what is true for the population?

24. Do at least 30% of the population of Lafayette residents have pollen allergies?

25. Are gender and type of allergy (pet, dust, pollen) related in the population?

26. Does increasing the number of ounces of water a person drinks decrease a person’s calorie consumption on a daily basis in the population?

27. Does the type of class activity (lab, homework, lecture) used to teach a concept make a difference to the population average quiz score on that activity?

28. What is the minimum score on this exam?

29. Is the population percentage of students passing this exam higher for students who did their practice problems than for those who didn’t?

30. Is the population average number of ounces of water a college student drinks daily less than the 64 ounces recommended by health experts?

So how do you know which is which? Start by deciding whether your variable(s) is/are categorical or quantitative. The first 2 are statistics, the rest are inference techniques.

Mean and/or standard deviation: just looking for a summary statistic, variable is quantitative

Five-number summary: Min, Q1, M, Q3, Max, summary statistics for a quantitative variable

Simple linear regression: using x to predict y, are x and y independent?, x and y are correlated, as x increases what happens to y, x and y are both quantitative variables

Multiple linear regression: similar to simple linear regression except there will be more than one x, all variables will be quantitative

1-sample mean t-test: comparing a single mean to a number, each unit is asked a numerical question (“how many times a week do you ride the bus?”), don’t know the population standard deviation, quantitative variable

Matched pairs t-test: before and after, left and right, all units are tested twice (a unit could be a pair of subjects or pair of units) and measurements are compared to each other, average difference, quantitative variable

Comparison of means t-test: 2 distinct populations with samples chosen independently, each unit is measured only once, one quantitative variable (your measurement) and one categorical variable (how you distinguish between your groups, like gender or eye color)

1-sample proportion Z-test: each unit is asked a yes/no question (“did you ride the bus today?”), proportion comes from taking the # of successes / # of trials, comparing a proportion or percentage to a number between 0 and 1

2-sample proportion Z-test: similar to 1-sample proportion Z-test except there are 2 distinct populations with samples selected independently so that the proportions can be compared to each other

Chi-squared test: 2 categorical variables, testing whether there is an association between the variables

One-way ANOVA: one categorical variable (how you distinguish between your groups) and one quantitative variable (your measurement), similar to comparison of means t-test except you can have more than 2 groups to compare

Two-way ANOVA: two categorical variables (how you distinguish between your groups) and one quantitative variable (your measurement), similar to doing one-way ANOVA twice except you can also look for the interaction between the two categorical variables

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