Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.89 versus H₁: p=0.89 n = 500, x=440, α = 0.01 Is npo (1-Po) 210? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) OA. Yes, because npo (1-P) = OB. No, because npo (1-P) =

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**Hypothesis Testing Using the P-Value Approach**

To test the hypothesis using the P-value approach, we have the following setup:

- Null hypothesis (\(H_0\)): \( p = 0.89 \)
- Alternative hypothesis (\(H_1\)): \( p \neq 0.89 \)

Given data:
- Sample size (\(n\)): 500
- Number of successes (\(x\)): 440
- Significance level (\(\alpha\)): 0.01

**Verification Requirement**

We need to verify that \(np_0(1 - p_0) \geq 10\). Please select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.)

- A. Yes, because \(np_0(1 - p_0) =\) [ ]
- B. No, because \(np_0(1 - p_0) =\) [ ] 

Please compute \(np_0(1 - p_0)\) with the given values to verify the requirement.
Transcribed Image Text:**Hypothesis Testing Using the P-Value Approach** To test the hypothesis using the P-value approach, we have the following setup: - Null hypothesis (\(H_0\)): \( p = 0.89 \) - Alternative hypothesis (\(H_1\)): \( p \neq 0.89 \) Given data: - Sample size (\(n\)): 500 - Number of successes (\(x\)): 440 - Significance level (\(\alpha\)): 0.01 **Verification Requirement** We need to verify that \(np_0(1 - p_0) \geq 10\). Please select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) - A. Yes, because \(np_0(1 - p_0) =\) [ ] - B. No, because \(np_0(1 - p_0) =\) [ ] Please compute \(np_0(1 - p_0)\) with the given values to verify the requirement.
Expert Solution
Step 1: Given data,

H y p o t h e s i s colon
H subscript 0 colon p equals 0.89
H subscript 1 colon p space not equal to 0.89

A space s a m p l e space s i z e colon
n equals 500

f a v o r a b l e space o u t c o m e s colon
x equals 440

T h e space l e v e l space o f space s i g n i f i c a n c e colon
alpha equals 0.01

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Follow-up Question
**Hypothesis Testing Using the P-value Approach**

**Objective:**
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.

**Hypotheses:**
- Null Hypothesis (\(H_0\)): \(p = 0.89\)
- Alternative Hypothesis (\(H_1\)): \(p \neq 0.89\)

**Given:**
- Sample size (\(n\)) = 500
- Number of successes (\(x\)) = 440
- Significance level (\(\alpha\)) = 0.01

**Step 1: Verify Conditions**

Determine if \(np_0(1 - p_0) \geq 10\).

1. Calculate \(np_0(1 - p_0)\):
   \[
   np_0(1 - p_0) = 48.95
   \]

Choice A is chosen: *Yes, because \(np_0(1 - p_0) = 48.95\).*

**Step 2: Find \(\hat{p}\)**

Calculate the sample proportion (\(\hat{p}\)):
- \(\hat{p} = 0.88\)

**Step 3: Find the Test Statistic \(z_0\)**

Calculate the test statistic:
- \(z_0 = -0.72\)
  - (Rounded to two decimal places as needed.)

**Step 4: Find the P-value**

The P-value will need to be calculated to three decimal places as needed.

---

**Summary:**

This step-by-step guide helps in conducting a hypothesis test using the P-value approach by verifying the necessary conditions, calculating the sample proportion, finding the test statistic, and determining the P-value. Ensure all values are rounded to the specified precision for accuracy.
Transcribed Image Text:**Hypothesis Testing Using the P-value Approach** **Objective:** Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. **Hypotheses:** - Null Hypothesis (\(H_0\)): \(p = 0.89\) - Alternative Hypothesis (\(H_1\)): \(p \neq 0.89\) **Given:** - Sample size (\(n\)) = 500 - Number of successes (\(x\)) = 440 - Significance level (\(\alpha\)) = 0.01 **Step 1: Verify Conditions** Determine if \(np_0(1 - p_0) \geq 10\). 1. Calculate \(np_0(1 - p_0)\): \[ np_0(1 - p_0) = 48.95 \] Choice A is chosen: *Yes, because \(np_0(1 - p_0) = 48.95\).* **Step 2: Find \(\hat{p}\)** Calculate the sample proportion (\(\hat{p}\)): - \(\hat{p} = 0.88\) **Step 3: Find the Test Statistic \(z_0\)** Calculate the test statistic: - \(z_0 = -0.72\) - (Rounded to two decimal places as needed.) **Step 4: Find the P-value** The P-value will need to be calculated to three decimal places as needed. --- **Summary:** This step-by-step guide helps in conducting a hypothesis test using the P-value approach by verifying the necessary conditions, calculating the sample proportion, finding the test statistic, and determining the P-value. Ensure all values are rounded to the specified precision for accuracy.
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Follow-up Question
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
Ho: p=0.89 versus H₁: p#0.89
1
= 500, x= 440, a = 0.01
Is npo (1-Po) ²10? Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or a decimal. Do not round.)
A. Yes, because npo (1-Po) = 48.95
OB. No, because npo (1-Po) =
Now find p
p= 0.88 (Type an integer or a decimal. Do not round.)
Find the test statistic zo.
Zo = (Round to two decimal places as needed.)
W
---
Transcribed Image Text:Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. Ho: p=0.89 versus H₁: p#0.89 1 = 500, x= 440, a = 0.01 Is npo (1-Po) ²10? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. Yes, because npo (1-Po) = 48.95 OB. No, because npo (1-Po) = Now find p p= 0.88 (Type an integer or a decimal. Do not round.) Find the test statistic zo. Zo = (Round to two decimal places as needed.) W ---
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Follow-up Question
**Hypothesis Testing Using the P-Value Approach**

*Question:*

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.

- Null Hypothesis (\(H_0\)): \(p = 0.89\) 
- Alternative Hypothesis (\(H_1\)): \(p \neq 0.89\) 
- Sample size (\(n\)): 500
- Number of successes (\(x\)): 440
- Significance level (\(\alpha\)): 0.01

**Verification:**

Check if \(np_0(1 - p_0) \geq 10\). Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.)

- A. Yes, because \(np_0(1 - p_0) = 48.95\). [This option is selected]
- B. No, because \(np_0(1 - p_0) = \_\_\_ \).

**Next Step:**

Now find \(\hat{p}\).

- \(\hat{p} = \_\_\_\) (Type an integer or a decimal. Do not round.)
Transcribed Image Text:**Hypothesis Testing Using the P-Value Approach** *Question:* Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. - Null Hypothesis (\(H_0\)): \(p = 0.89\) - Alternative Hypothesis (\(H_1\)): \(p \neq 0.89\) - Sample size (\(n\)): 500 - Number of successes (\(x\)): 440 - Significance level (\(\alpha\)): 0.01 **Verification:** Check if \(np_0(1 - p_0) \geq 10\). Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) - A. Yes, because \(np_0(1 - p_0) = 48.95\). [This option is selected] - B. No, because \(np_0(1 - p_0) = \_\_\_ \). **Next Step:** Now find \(\hat{p}\). - \(\hat{p} = \_\_\_\) (Type an integer or a decimal. Do not round.)
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