91Ó°ÊÓ

given,

The test hypothesis:

$H_0$: The data provides sufficient evidence to show that the dice were not loaded, that is, all six numbers have equal probability.

$H_a$: The data provide sufficient evidence to indicate that the die is loaded

Calculating the Goodness of fit:

$∑\frac{(Obs−Exp{)}^2}{\mathrm{Exp}}=2.48$

$$\begin{gathered} =k-1 \\ =6-1 \\ =5 \end{gathered}$$

Critical value is ${\mathrm{χ}}_{0.05}^{2}5df\text{is}11.070$

The value of the test statistic is,

$X^2=2.48$

${\mathrm{χ}}^2=2.48<{\mathrm{χ}}_{0.05}^2=11.070$, because it does not fall in the rejection region.

Thus, we do not reject the null hypothesis, $H_0$

Therefore, we do not reject localid="1652033723048" $H_0:H_0$Variable distribution of the given problem.

Therefore, the data provide sufficient evidence to show that the dice were not loaded, that is, all six numbers have the same probability.

And, The data do not provide sufficient evidence to show that deaths were loaded at a 5% value.

localid="1652033609570" $\begin{array}{r}=11.070\\ {\mathrm{χ}}^2<11.070\\ p=0.780>0.05\\ \mathrm{So},{\mathrm{H}}_{\mathrm{O}}\text{should be rejected.}\end{array}$

The data do not provide sufficient evidence to conclude that the die is loaded at $0.05$of significance.