Questions: The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H, when the level of significance is (a) α=0.01, (b) α=0.05, and (c) α=0.10. P=0.0463 (a) Do you reject or fail to reject H₀ at the 0.01 level of significance? A. Reject to, because the P-value, 0.0463, is less than α=0.01. B. Fail to reject H₀ because the P-value, 0.0463, is greater than α=0.01. C. Reject H₀ because the P-value, 0.0463, is greater than α=0.01. D. Fail to reject H₀ because the P-value, 0.0463 is less than α=0.01. (b) Do you reject or fail to reject H₀, at the 0.05 level of significance? A. Reject to, because the P-value, 0.0463, is less than α=0.05. B. Fail to reject H₀ because the P-value, 0.0463 is less than α=0.05. C. Reject H₀ because the P-value, 0.0463 is greater than α=0.05 D. Fail to reject H₀ because the P-value, 0.0463, is greater than α=0.05. (c) Do you reject or fail to reject H₀ at the 0.10 level of significance? A. Reject to because the P-value, 0.0463, is greater than α=0.10. B. Fail to reject H₀ because the P-value, 0.0463 is less than α=0.10. C. Fail to reject H₀ because the P-value, 0.0463, is greater than α=0.10.

The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H, when the level of significance is (a) α=0.01, (b) α=0.05, and (c) α=0.10.
P=0.0463
(a) Do you reject or fail to reject H₀ at the 0.01 level of significance?
A. Reject to, because the P-value, 0.0463, is less than α=0.01.
B. Fail to reject H₀ because the P-value, 0.0463, is greater than α=0.01.
C. Reject H₀ because the P-value, 0.0463, is greater than α=0.01.
D. Fail to reject H₀ because the P-value, 0.0463 is less than α=0.01.
(b) Do you reject or fail to reject H₀, at the 0.05 level of significance?
A. Reject to, because the P-value, 0.0463, is less than α=0.05.
B. Fail to reject H₀ because the P-value, 0.0463 is less than α=0.05.
C. Reject H₀ because the P-value, 0.0463 is greater than α=0.05
D. Fail to reject H₀ because the P-value, 0.0463, is greater than α=0.05.
(c) Do you reject or fail to reject H₀ at the 0.10 level of significance?
A. Reject to because the P-value, 0.0463, is greater than α=0.10.
B. Fail to reject H₀ because the P-value, 0.0463 is less than α=0.10.
C. Fail to reject H₀ because the P-value, 0.0463, is greater than α=0.10.
Transcript text: The Pyalue for a hypothesis lest is shown. Use the Pvalue to decide whether to reject $H$, when the level of signifcance is (a) $\alpha=0.01$, ( $(\mathrm{b}) \mathrm{a}=0.05$, and (c) $\alpha=0.10$. \[ P=0.0463 \] (a) Do you reject or tall to reject $H_{6}$ at the 0.01 level of signifiance? A. Reject to, because the Pralue, 0.0463 , is less than $\alpha=0.01$. B. Fall to reiect $\mathrm{H}_{\mathrm{j}}$ because the $P$ yalue, 0.0463 , is greater than $\mathrm{a}=0.01$. C. Reject $\mathrm{H}_{0}$ because the Pvalue, 0.0463 , is greater than $\mathrm{q}=0.01$. D. Fal to reject H0 because the $P$-value, 0.0463 is less than $\alpha=0.01$. (o) Do you reject or fail to reject $\mathrm{H}_{\mathrm{b}}$, at the 0.05 level of signicance? A. Reject to, because the Pralue. 0.0463 , is less than $a=0.05$. B. Fal to reject $H_{0}$ because the $P$ value, 0.0463 is less than $\alpha=0.05$. C. Reject $\mathrm{H}_{6}$ because the Pvalue. 0.0463 is greater than $\mathrm{a}=0.05$ D. Falt to reject $H_{0}$ because the P-value, 0.0463 , is greater than $\alpha=0.05$. (c) Do you reject or tall to reject $H_{0}$ at the $Q .10$ level of signilicance? A Refect thb because the Pralue, 0.0463 , is greater than $\alpha=0.10$. B. Fal to reject $H_{0}$ because the Pvalue, 0.0463 is less than $a=0.10$. C. Fall to reject $H_{0}$ because the $P$ value, 0.0463 , is greater than $a=0.10$
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Solution

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Solution Steps

To determine whether to reject or fail to reject the null hypothesis \( H_0 \), compare the given p-value (0.0463) with the significance levels (\(\alpha\)) provided in each part of the question. If the p-value is less than \(\alpha\), reject \( H_0 \); otherwise, fail to reject \( H_0 \).

Step 1: Evaluate at \( \alpha = 0.01 \)

Given the p-value \( P = 0.0463 \) and the significance level \( \alpha = 0.01 \): \[ P > \alpha \implies 0.0463 > 0.01 \] Thus, we fail to reject \( H_0 \).

Step 2: Evaluate at \( \alpha = 0.05 \)

Now, using \( \alpha = 0.05 \): \[ P < \alpha \implies 0.0463 < 0.05 \] Therefore, we reject \( H_0 \).

Step 3: Evaluate at \( \alpha = 0.10 \)

Finally, for \( \alpha = 0.10 \): \[ P < \alpha \implies 0.0463 < 0.10 \] Hence, we reject \( H_0 \).

Final Answer

  • For \( \alpha = 0.01 \): Fail to reject \( H_0 \)
  • For \( \alpha = 0.05 \): Reject \( H_0 \)
  • For \( \alpha = 0.10 \): Reject \( H_0 \)

The answers are:

  • \( \alpha = 0.01 \): \(\boxed{\text{Fail to reject } H_0}\)
  • \( \alpha = 0.05 \): \(\boxed{\text{Reject } H_0}\)
  • \( \alpha = 0.10 \): \(\boxed{\text{Reject } H_0}\)
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