91Ó°ÊÓ

Given in the question that, The P-value for a two-sided test of the null hypothesis $H_0:\mathrm{μ}=10$is $0.06$.

we need to find that Whether the$95\%$confidence interval for $\mathrm{μ}$include $10$.

$H_0:\mathrm{μ}=10$

$P-$value $=0.06$

Reject, $H_0$, if level of significance$\left(\mathrm{Î\pm }\right)<P-$value .

The null and alternative hypotheses could be written as:

$H_0:\mathrm{μ}=10$

$H_a:\mathrm{μ}≠10$

The level of significance is$0.05$

Here,

$p-$value $(0.06)>\mathrm{Î\pm }(0.05)$

Thus, the null hypothesis is not rejected. So, it could be concluded that $95\%$confidence interval for $\mathrm{μ}$will includes $10$

Given in the question that, The $P$-value for a two-sided test of the null hypothesis $H_0:\mathrm{μ}=10$is $0.06$.

We need to find that Whether the$90\%$confidence interval for $\mathrm{μ}$include$10$.

Here,

$H_0:\mathrm{μ}=10$

$P$-value$=0.06$

Reject, $H_0$, if level of significance $\left(\mathrm{Î\pm }\right)<P-$value

The null and alternative hypotheses could be written as:

$H_0:\mathrm{μ}=10$

$H_a:\mathrm{μ}≠10$

The level of significance is $0.10$.

Here, $p-$value $(0.06)<\mathrm{Î\pm }(0.10)$

Thus, the null hypothesis is rejected. So, it could not be concluded that $90\%$confidence interval for $\mathrm{μ}$ will include$10.$