91Ó°ÊÓ

Consider the given question,

Null Hypothesis is the satisfaction levels are not differing among the three categories of people, $$\begin{gathered} H_0:R=B \\ =P \end{gathered}$$

Alternate Hypothesis is the satisfaction levels are not differing among the three categories of people, $$\begin{gathered} H_1:R≠B \\ ≠P \end{gathered}$$

According to the decision rule,

When P-value is less than the Level of significance then it results in the rejection of the null hypothesis.

When the test statistics value is greater than the tabulated value then reject the null hypothesis.

On calculating the $x^2$test,

Chi-square$=7.05$,

$df=6$,

p-value$=0.3162$

Consider the above table,

$$\begin{gathered} x^2=\underset{}{∑}\frac{{\left(O-E\right)}^2}{E} \\ =7.05 \end{gathered}$$

Hence, we know $$\begin{gathered} x^2=7.05, \\ P-value=0.3162 \end{gathered}$$.

Compare $x^2$-test value and critical value with $$\begin{gathered} \left(r-1\right)×\left(c-1\right)=\left(4-1\right)×\left(3-1\right) \\ =6 \end{gathered}$$at $10\%$level of significance is role="math" localid="1651939512728" $10.6446,7.05<10.6446$, fail to reject null hypothesis.

Therefore, on concluding, we can say that the satisfaction levels are not differing among the three categories of people.