$$ 1 \leftarrow \quad \begin{array}{l} ext { The test statistic of } z=0.59 ext { is obtained when testing the claim that } p0.7 ext {. } \ ext { a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. } \ ext { b. Find the } P ext {-value. } \ ext { c. Using a significance level of } \alpha=0.10 ext {, should we reject } H_{0} ext { or should we fail to reject } H_{0} ext { ? } \ ext { Click here to view page } 1 ext { of the standard normal distribution table. } \ ext { Click here to view page } 2 ext { of the standard normal distribution table. } \ ext { a. This is a right-tailed test. } \ ext { b. } P ext {-value }=\square ext { (Round to three decimal places as needed.) }\end{array} $$.

Question

$$ 1 \leftarrow \quad \begin{array}{l}	ext { The test statistic of } z=0.59 	ext { is obtained when testing the claim that } p>0.7 	ext {. } \ 	ext { a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. } \ 	ext { b. Find the } P 	ext {-value. } \ 	ext { c. Using a significance level of } \alpha=0.10 	ext {, should we reject } H_{0} 	ext { or should we fail to reject } H_{0} 	ext { ? } \ 	ext { Click here to view page } 1 	ext { of the standard normal distribution table. } \ 	ext { Click here to view page } 2 	ext { of the standard normal distribution table. } \ 	ext { a. This is a right-tailed test. } \ 	ext { b. } P 	ext {-value }=\square 	ext { (Round to three decimal places as needed.) }\end{array} $$.

UpStudy AI · Accepted Answer

**a. Identification of the Hypothesis Test**

Since the claim is $$ p>0.7 $$, the alternative hypothesis is one‐sided with a greater than sign. Therefore, the test is a right-tailed test.

**b. Finding the $$ P $$-value**

The test statistic is given as $$ z = 0.59 $$. For a right-tailed test, the $$ P $$-value is calculated as:
$$
P\text{-value} = 1 - \Phi(0.59)
$$
where $$\Phi(z)$$ is the cumulative distribution function of the standard normal distribution.

Using the standard normal table, we find:
$$
\Phi(0.59) \approx 0.7224
$$
Thus, 
$$
P\text{-value} \approx 1 - 0.7224 = 0.2776
$$
Rounded to three decimal places, the $$ P $$-value is approximately $$ 0.278 $$.

**c. Decision at $$ \alpha = 0.10 $$**

Since the $$ P $$-value ($$ 0.278 $$) is greater than the significance level $$ \alpha = 0.10 $$, we do not have sufficient evidence to reject the null hypothesis.

Therefore, we fail to reject $$ H_0 $$.
**a. This is a right-tailed test.** **b. $$ P $$-value ≈ 0.278** **c. We fail to reject $$ H_0 $$ at $$ \alpha = 0.10 $$.

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