Question

Teenage suicide is a serious problem in the United States. The family economic status of a sample of 38 teenage who committed suicide was distributed as follows:

ClassUpperUpper MiddleLower MiddleLowerNumber of Suicides141086

Is there statistical evidence that the proportions in the classes differ at alpha 0.05?

1. Formulate the H₀ and H₁
2. C.V. at alpha 0.05 level of significance
3. Compute the test value: Chi-square X²
4. Decision
5. Interpretation

Answer 1

1.

$H_0:$ the proportions in the classes do not differ

$H_a:$ the proportions in the classes differ

2.

(Rows-1)*(Columns-1) = (2-1)*(2-1) = 1

critical value:

$\chi^2_{crit}=3.84$

3.

$\chi^2=\sum \frac{(O_i-E_i)^2}{E_i}=0.005$

where $O_i$ is observed frequency,

$E_i$ = (row total)(column total)/(total) is expected frequency

4.

Since $\chi^2<\chi^2_{crit}$ we accept null hypothesis

5.

The proportions in the classes do not differ.