Question

A market research firm also wants to pilot test a new line of vehicles among prospective customers. They collect data on attitude ratings (higher scores reflect more liking) for four different car models and find the following results: Toyota Camry (M = 8.2; N = 50), Honda Accord (M= 7.5; N = 50), Ford Focus (M = 4.0; N = 50), and Chevrolet Impala (M=5.7; N = 50). They also calculated the between-group and total sum of squares (SS_B = 568.6; SS_T = 7781.4). Use a one-way ANOVA (where α = .01) to determine if there are significant differences in ratings of cars.

        12. Identify the alternative hypothesis (F tests are always nondirectional)

       13. List your degrees of freedom (within)

       14. List your degrees of freedom (between)

       15. List your mean squares between groups

       16. List your mean squares within groups

       17. List your F test statistic

       18. List your critical F value

       19. Are there statistically significant differences in ratings among different cars? (Yes/No)

       20. Calculate partial eta-squared (η²) for the effect of car type on liking ratings (list as decimal, 0.xx)

       21. Calculate Tukey’s HSD

       22. Use Tukey’s HSD to determine if the difference in liking ratings between the Toyota Camry and Ford Focus is statistically significant (Yes/No)

You can use the table below to help answer the questions in this scenario

Source	SS	df	MS	F
Between
Within
Total

Answer 1

12. Alternate Hypothesis: There is significant differences in ratings of the cars

13. df (Between) = I - 1 = 4 - 1 = 3

Here, I = no. of groups

14. df (within) = N - I = 200 - 4 = 196

15. MS(Between) = SS/df = 568.6/3 = 189.53

16. MS(Error) = SS/df = 7212.8/196 = 36.8

17. F test statistic = MS (between)/MS (Error) = 5.15

18. F-critical value at (0.01, 3, 196) is 3.883

The ANOVA table filled is:

Source	SS	df	MS	F	F-critical
Between	568.6	3	189.5333	5.150362	3.883
Within	7212.8	196	36.8
Total	7781.4	199

19. As F>Fc, we can reject the null hypothesis and say that there is significant differences in the ratings among different cars.

20. partial eta-squared (η²) = SS(between)/SS(total)

= 568.6/7781.4

η² = 0.07

21. The formula for Tukey HSD is:

q-value from the table = 4.497

Nk = subjects in each category = 50

HSD = 3.86

22. Difference in means of toyota camry and ford focus = 8.2 - 4.0 = 4.2

As the difference>Tukey HSD, we can say that the difference between the ratings of the two cars is statistically significant.