Question

Distribution $0.5,0.3,0.2$.

observed frequencies $45,39,16$.

Significant level$\alpha =0.01$.

Short answer

The variable has a given distribution$0.5,0.3,0.2$.

Step-by-step solution

Given Information

Given data:

Distribution $0.5,0.3,0.2$.

observed frequencies $45,39,16$.

Significant level $\alpha =0.01$.

Explanation

To find the goodness fit test,

No. of. Sample size $n=45+39+16$

$n=100$.

$\begin{array}{|lllll|}\hline \text{Observed frequencies}& 45& 39& 16& \\ \text{Relative frequenciesp}& 0.5& 0.3& 0.2& \\ \text{Expected frequencies}np& 50& 30& 20& \\ \frac{(obs-\exp {)}^2}{\exp }& 0.5& 2.9& 0.8& {\chi }^2=\sum \frac{(obs-\exp {)}^2}{\exp }=4.2\\ \hline\end{array}$

The degree of freedom,

$=k-1$

$=3-1$

$=2$

Explanation

The critical value, with $2df$is ${\chi }_{0,01}^2=9.210$

${\chi }^2=4.2<{\chi }^{2}0,05=9.210$

Because it isn't available in the rejection area. So the Null hypothesis is accepted.

As a result, the variable has a defined area.

The $P$value is:$0.010$