## Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

a. State the hypotheses and identify the claim. $H_o:$ the proportions are the same from those in the report $H_a:$ the proportions differ from those in the report (claim) b. Find the critical value(s). At $\alpha=0.05, n=3, df=2, \chi^2_c=5.991$ c. Compute the test value. The observed proportions are $35/120=0.292, 78/120=0.65, 7/120=0.058$ $\chi^2=\frac{(0.292-0.3158)^2}{0.3158}+\frac{(0.65-0.5983)^2}{0.5983}+\frac{(0.058-0.0859)^2}{0.0659}=0.015$ d. Make the decision. As $\chi^2<5.991$, we do not reject the null hypothesis. e. Summarize the results. At $\alpha=$ 0.05, there is not sufficient evidence that the proportions differ from those in the report.