Question

A researcher is interested in examining whether different practice strategies have an influence on the accuracy of basketball players' free throws. The researcher collected data from a sample of 18 participants who were classified in one of three groups: (1) 6 players who r eceived no special practice, (2) 6 players who spent 30 minutes just imagining that they were shooting baskets, and (3) 6 players who spent 30 minutes actually practicing shooting baskets. After participating in the experiment for two weeks, the players attempted 10 free throws. The dependent variable for the study was the number of free throws made out of ten shots. e researcher selected an alpha level of .01. The researcher found the following descriptive statistics: 1. Participants who received no special practice made an average of 3.50 free throws (SD 1.38) 2. Participants who imagined shooting baskets made an average of 5.00 free throws (SD 1.26) 3. Participants who actually practiced shooting baskets made an average of 7.00 free throws (SD 89) e researcher then ran an analysis of variance to determine whether at least two of these means were significantly different. The researcher found the following: Th 1. Sum of squares between groups -37 2. Sum of squares within groups 21.45 Based on this information, match each of the following with the correct answer:

Answer 1

a) degrees of freedom between group = k -1 = 3-1 = 2

b) degrees of freedom within group = n-k = 18-3 = 15

c) mean square between groups = SS_ between/ df_between = 37/2 = 18.5

d) mean square within group = SS_within/df_within = 21.45/15 = 1.4

e) obtained F value = MS_ between/MS_ within = 18.5/1.4 = 13.2143

f) critical f value = F(a,df_ between, df_ within) = F(0.01,2,15) =  =F.INV(1-0.01,2,15) = 6.3589

g) Since F > F(0.01,2,15), I REJECT ho at 1% level of significance and conclude that the results are significant. in other words I can say that at least one of the mean accuracy differ significantly in the three practice strategy.