## 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 not different from those from the U.S. Department of Labor $H_a:$ the proportions are different from those from the U.S. Department of Labor (claim) b. Find the critical value(s). $\alpha=0.01, n=3, df=2, \chi^2_c=9.210$ c. Compute the test value. The observed values are $87, 53, 40$ The expected values are $180\times0.448=80.64, 180\times0.252=45.36, 180\times0.3=54$ $\chi^2=\frac{(87-80.64)^2}{80.64}+\frac{(53-45.36)^2}{45.36}+\frac{(40-54)^2}{54}=11.8$ d. Make the decision. $\chi^2>9.21$ we should reject the null hypothesis. e. Summarize the results. At the 0.01 level of significance, the proportions are different from those from the U.S. Department of Labor.