Q.86 - The Practice of Statistics for AP

Question

Tests and CIs The P-value for a one-sided test of the null hypothesis$H_0:\mu =15$ is $0.03$.

(a) Does the $99\%$ confidence interval for $\mu$ include $15$ ? Why or why not?

(b) Does the $95\%$ confidence interval for $\mu$include $15$? Why or why not?

Step-by-Step Solution

Answer

(a)The $99\%$confldence interval for $\mu$ include $15$.

(b)the$95\%$ confldence interval for $\mu$ include $15.$

Part (a) Step 1: Given information

Given in the question that, The P-value for a one-sided test of the null hypothesis $H_0:\mu =15$ is $0.03$.

We need to flnd that Whether the $99\%$ confldence interval for $\mu$ include $15$ .

Part (a) Step 2: Explanation

$P$-value is $0.03$

Confidence level $=99\%$

Reject the null hypothesis, if$P-$value is less than the significance level.

The level of significance is:

Level of significance$\left(\alpha \right)=1-$ Confidence level

$=1-0.99$

$=0.01$

The null and alternative hypotheses are:

$H_0:\mu =15$

$H_a:\mu \ne 15$

Here $P$-value $(0.03)>\alpha (0.01)$. The null hypothesis is not rejected. Thus, it could be said that the confidence level would contain$15 .$

Part (b) Step 1: Given information

Given in the question that,  The $P$-value for a one-sided test of the null hypothesis $H_0:\mu =15$ is $0.03$.

We need to flnd that Whether the$95\%$ confldence interval for $\mu$ include

$15$.

Part (b) Step 2: Explanation

Confidence level $=95\%$

Reject the null hypothesis, if $\mathrm{P}$-value is less than the significance level.

The level of significance is:

Level of significance $\left(\alpha \right)=1$ - Confidence level

$=1-0.95$

$=0.05$

The null and alternative hypotheses are:

$H_0:\mu =15$

$H_a:\mu \ne 15$

Here $\mathrm{P}$-value$(0.03)<\alpha (0.05)$. The null hypothesis is rejected. Thus, it could not be said that the confidence level would contain$15$.