Answer
Step 1:
$H_0$ : The proportions of the services provided to low income children up to the age of 5 years and their families are as follows: 4% 5 year-olds, 52% four-year-olds, 34% three-year-olds, and 10% under 3 years.
$H_1$: The distribution is not the same as stated in the null hypothesis.
Step 2:
Since α=0.05, and the degrees of freedom are 4-1=3 , the critical value is 7.815
Step 3:
Expected Value:
0.04 * 200 = 8
0.52 * 200 = 104
0.34 * 200 =68
0.10 * 200 =20
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$ =$\frac{(20-8)^{2}}{8}$ + $\frac{(120-104)^{2}}{104}$ + $\frac{(40-68)^{2}}{68}$ + $\frac{(20-20)^{2}}{20}$
=18+2.4622+11.529+0
=31.991
Step 4:
Since P(Χ2 > 31.991) = 0 < α, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to reject the claim and hence we conclude that the proportions are differ from the programs.
