Answer
No. Yes. see explanations.
Work Step by Step
a. State the hypotheses and identify the claim.
$H_o:$ At $\alpha=$ 0.10, the distribution is as stated
$H_a:$ At $\alpha=$ 0.10, the distribution is not as stated (claim)
b. Find the critical value(s).
$\alpha=0.10, n=3, df=2, \chi^2_c=4.605$
c. Compute the test value.
The observed values are $120 42 38$
The expected values are $200\times0.75=150, 200\times0.11=22, 200\times0.14=28$
$\chi^2=\frac{(120-150)^2}{150}+\frac{(42-22)^2}{22}+\frac{(38-28)^2}{28}=27.75$
d. Make the decision.
As $\chi^2>4.605$ we reject the null hypothesis.
e. Summarize the results.
At $\alpha=$ 0.10, it can be concluded that the distribution is not as stated.
Yes. In a rural area, the percentages for the different reasons to deny applications may be different.
