Answer
No.
Work Step by Step
a. State the hypotheses and identify the claim.
$H_o:$ At α=0.01, the proportions of female students who work are equal. (claim)
$H_a:$ At α=0.01, the proportions of female students who work are not equal.
b. Find the critical value(s).
$\alpha=0.01, df=(2-1)(3-1)=2, \chi^2_c=9.210$
c. Compute the test value.
Calculate the expected values (in parenthesis) with the known average of working students.
Work 45 (28.8) 31 (28.8) 38 (28.8)
Don't work 35 (51.2) 49 (51.2) 42 (51.2)
Calculate $\chi^2=\frac{(O-E)^2}{E}=19.1$ which gives $P<0.005$
d. Make the decision.
$P<0.01$ we reject the null hypothesis.
e. Summarize the results.
At α=0.01, the proportions of female students who work are not equal.
