Question

Distribution $0.2,0.1,0.1,0.3,0.3$.

observed frequencies $9,7,1,12,21$..

Significant level $\alpha =0.10$.

Short answer

The variable has given distribution.$0.2,0.1,0.1,0.3,0.3$

Step-by-step solution

Given Information

Distribution $0.2,0.1,0.1,0.3,0.3$.

observed frequencies $9,7,1,12,21$..

Significant level $\alpha =0.10$.

Explanation

To find the goodness fit test,

No. of. Sample size $=9+7+1+12+21$.

$\begin{array}{|lccccll|}\hline \text{Observed frequencies}& 9& 7& 1& 12& 21& \\ \text{Relative frequenciesp}& 0.2& 0.1& 0.1& 0.3& 0.3& \\ \text{Expected frequencies}np& 10& 5& 5& 15& \mathrm{v}& \\ \frac{(obs-\exp {)}^2}{\exp }& 0.1& 0.8& 3.2& 0.6& 2.4& {\chi }^2=\sum \frac{(obs-\exp {)}^2}{\exp }=7.1\\ \hline\end{array}$

Degrees of freedom,

$=k-1$

$=5-1$

$=4$

Explanation

The critical value, with $4df$is ${\chi }^{2}0,10=7.779$

${\chi }^2=7.1<{\chi }^{2}0,10=7.779$

Because it does not comes in the rejection region. To accept the Null hypothesis $H_0$.

$H_0$has distribution in the given problem.

Therefore, the variable has given distribution.

The $p$value is: $0.1306$$0.1306$