Questions: The test statistic of z=1.43 is obtained when testing the claim that p>0.2. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. c. Using a significance level of α=0.10, should we reject H0 or should we fail to reject H0? a. This is a right-tailed test. b. P-value =0.076 (Round to three decimal places as needed.) c. Choose the correct conclusion below. A. Reject H0. There is sufficient evidence to support the claim that p>0.2. B. Reject H0. There is not sufficient evidence to support the claim that p>0.2. C. Fail to reject H0. There is not sufficient evidence to support the claim that p>0.2. D. Fail to reject H0. There is sufficient evidence to support the claim that p>0.2.

The test statistic of z=1.43 is obtained when testing the claim that p>0.2.
a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.
b. Find the P-value.
c. Using a significance level of α=0.10, should we reject H0 or should we fail to reject H0?
a. This is a right-tailed test.
b. P-value =0.076 (Round to three decimal places as needed.)
c. Choose the correct conclusion below.
A. Reject H0. There is sufficient evidence to support the claim that p>0.2.
B. Reject H0. There is not sufficient evidence to support the claim that p>0.2.
C. Fail to reject H0. There is not sufficient evidence to support the claim that p>0.2.
D. Fail to reject H0. There is sufficient evidence to support the claim that p>0.2.
Transcript text: The test statistic of $\mathrm{z}=1.43$ is obtained when testing the claim that $\mathrm{p}>0.2$. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the $P$-value. c. Using a significance level of $\alpha=0.10$, should we reject $H_{0}$ or should we fail to reject $H_{0}$ ? a. This is a right-tailed test. b. $P$-value $=0.076$ (Round to three decimal places as needed.) c. Choose the correct conclusion below. A. Reject $\mathrm{H}_{0}$. There is sufficient evidence to support the claim that $\mathrm{p}>0.2$. B. Reject $\mathrm{H}_{0}$. There is not sufficient evidence to support the claim that $\mathrm{p}>0.2$. C. Fail to reject $\mathrm{H}_{0}$. There is not sufficient evidence to support the claim that $\mathrm{p}>0.2$. D. Fail to reject $\mathrm{H}_{0}$. There is sufficient evidence to support the claim that $\mathrm{p}>0.2$.
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Solution

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Solution Steps

Step 1: Identify the Type of Hypothesis Test

The hypothesis test is identified as a right-tailed test since we are testing the claim that \( p > 0.2 \).

Step 2: Calculate the P-value

To find the P-value, we use the Z-score of \( z = 1.43 \). The P-value is calculated as follows:

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(\infty) - \Phi(1.43) = 0.924 \]

Step 3: Make a Decision Based on the Significance Level

Using a significance level of \( \alpha = 0.10 \), we compare the P-value to \( \alpha \):

\[ \text{Since } P = 0.924 > 0.10, \text{ we fail to reject } H_0. \]

This indicates that there is not sufficient evidence to support the claim that \( p > 0.2 \).

Final Answer

  • a. This is a right-tailed test.
  • b. P-value = 0.924
  • c. Fail to reject \( H_0 \). There is not sufficient evidence to support the claim that \( p > 0.2 \).

\(\boxed{\text{Answer is C}}\)

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