Answer
Yes.
Work Step by Step
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.
