# MATHEMATICS

12. Suppose we wanted to compare the somatic complaints (as measured on a scale known as the Physical Symptom Scale or PSS) of three groups of people: non-smokers, smokers, and people who recently quit smoking. Using the following data for PSS, do a one-way ANOVA to test the hypothesis that the population means are equal:

Nonsmokers Smokers Quitters

19 31 30

28 29 22

29 22 30

20 20 29

25 28 34

Using StatCrunch, determine the means for the three groups and compute the sums of squares, degrees of freedom, and mean squares for these data. What is the value of F? Using an alpha of 0.05, is the F statistic significant? Why? Copy and Paste your work from StatCrunch into your Word document submission.

TIP: Conduct a one-way ANOVA using STATCRUNCH

13. A new motorcycle is being developed to meet new gas mileage standards recently passed by the federal government. An engineer tested three model designs by randomly assigning the motorcycles in a blind study (the riders recorded the mileage but did not know the design of the motorcycle, only its code). The data in miles per gallon (MPG) for the three designs is listed below:

X-1 |
B-1 |
Z-1 |

45 | 55 | 54 |

62 | 55 | 52 |

50 | 54 | 41 |

65 | 44 | 40 |

62 | 52 | 38 |

50 | 69 | 39 |

50 | 58 | 51 |

58 | 45 | 64 |

Using StatCrunch, determine the means for the three groups and compute the sums of squares, degrees of freedom, and mean squares for these data. What are the hypotheses to be tested here? What is the value of *F*? Using an alpha of 0.05, is the *F* statistic significant? Why? Copy and Paste your work from StatCrunch into your Word document submission for full credit.

TIP: Another example using 1-way ANOVA in StatCrunch

14. For each of the following *F* values, indicate whether the *F* is statistically significant at the specified alpha level:

a. F = 4.80, df = 4, 40 α = 0.01

b. F = 5.00, df = 3, 60, α = 0.001

c. F = 3.45, df = 3, 27, α = 0.05

d. F = 1.99, df = 2, 150, α = 0.01

e. F = 3.09, df = 2, 250, α = 0.05

TIP: Use the textbook ANOVA tables on pages 413 to 415 [look to see if the alpha value for each of your F-statistic is correct for the table you have selected].

If the F-statistic is **GREATER** than the value in the critical/tabled value, the result is statistically significant.