The chess study discussed in this chapter (de Bruin et al., 2007) hypothesized that the number of checkmates should be greater for students asked to make predictions while learning to play chess than students who simply observe games of chess being played. Using the ANOVA summary table in Table 11.4(c), conduct an analytical comparison of the number of checkmates for the Prediction \((N=14, M=.86)\) versus Observation \((N=14\), \(M=1.36)\) conditions.

a. State the null and alternative hypotheses \(\left(\mathrm{H}_{0}\right.\) and \(\left.\mathrm{H}_{1}\right)\).

b. Make a decision about the null hypothesis.

(1) Calculate the degrees of freedom ( \(d f\) ).

(2) Set alpha ( \(\alpha\) ), identify the critical value, and state a decision rule.

(3) Calculate the \(F\)-ratio for an analytical comparison ( \(F_{\text {comp }}\) ).

(4) Make a decision whether to reject the null hypothesis.

(5) Determine the level of significance.

(6) Calculate a measure of effect size ( \(\left.R_{\text {comp }}^{2}\right)\).

c. Draw a conclusion from the analysis.

d. Relate the result of the analysis to the research hypothesis.