Steps in a Z Test Step 1: Determine the Null and Alternative Hypothesis Ho: p = or M1-M2 = 0 or M1-M2 # 0 Step 2: Two-tailed, Step 3: Select significant level, a Step 4: Z test Step 5: Find the critical value and determine if Zobt is in the “reject" or "fail to reject" region. Draw and label the graph. Level of Confidence Fail to Reject Reject Reject a/2 a/2 Zcrit =- Zcrit = Label the following: *a = 1- Confidence Level *oa/23area of each tail *Zcrit Table Confidence Level (CL) a = 1 - CL Zcrit 90% ( 0.90 ) 1- .90 = 0.10 +1.645 95% ( 0.95 ) +1.960 ±2.576 Step 6: Calculate the Test statistics (Zobt) N= X = Calculate. Zobt = 0/VN Step 7- 9: State the conclusion: There is statistically significant difference between the two means if the Null hypothesis rejected OR there is NO statistically significant difference between the two means if the Null hypothesis is not rejected (failed to be rejected).
Steps in a Z Test Step 1: Determine the Null and Alternative Hypothesis Ho: p = or M1-M2 = 0 or M1-M2 # 0 Step 2: Two-tailed, Step 3: Select significant level, a Step 4: Z test Step 5: Find the critical value and determine if Zobt is in the “reject" or "fail to reject" region. Draw and label the graph. Level of Confidence Fail to Reject Reject Reject a/2 a/2 Zcrit =- Zcrit = Label the following: *a = 1- Confidence Level *oa/23area of each tail *Zcrit Table Confidence Level (CL) a = 1 - CL Zcrit 90% ( 0.90 ) 1- .90 = 0.10 +1.645 95% ( 0.95 ) +1.960 ±2.576 Step 6: Calculate the Test statistics (Zobt) N= X = Calculate. Zobt = 0/VN Step 7- 9: State the conclusion: There is statistically significant difference between the two means if the Null hypothesis rejected OR there is NO statistically significant difference between the two means if the Null hypothesis is not rejected (failed to be rejected).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Steps in a Z Test
Transcribed Image Text:# T Table
This t-distribution table provides critical values of the t-statistic for various degrees of freedom (df) and confidence levels for two-tailed tests. The table is structured by cumulative probability levels commonly used in hypothesis testing: 0.10, 0.05, and 0.01.
## Table Structure
1. **Degrees of Freedom (df):** Listed in the first column, ranging from 1 to 1000.
2. **Cumulative Probability (cum. prob.) Columns:**
- **t₀.₁₀ (0.10 cumulative probability)**
- **t₀.₀₅ (0.05 cumulative probability)**
- **t₀.₀₁ (0.01 cumulative probability)**
## Example Entries:
- For df = 1:
- t₀.₁₀ = 6.314
- t₀.₀₅ = 12.71
- t₀.₀₁ = 63.66
- For df = 30:
- t₀.₁₀ = 1.697
- t₀.₀₅ = 2.042
- t₀.₀₁ = 2.750
- For df = 1000:
- t₀.₁₀ = 1.646
- t₀.₀₅ = 1.962
- t₀.₀₁ = 2.581
## Confidence Level
- **z-values for standard normal distribution** (at the bottom of the table):
- 90% confidence level: z = 1.645
- 95% confidence level: z = 1.960
- 99% confidence level: z = 2.576
This table is essential for conducting t-tests in statistics, helping to determine critical values needed to assess the significance of a result compared to a null hypothesis.
![Certainly! Here's a transcription of the text along with a detailed explanation of the graph for educational purposes.
---
**Steps in a Z Test**
**Step 1:** Determine the Null and Alternative Hypothesis
- \(H_0: \mu = \) [Blank] or \(M_1 - M_2 = 0\)
- \(H_a: \mu \neq \) [Blank] or \(M_1 - M_2 \neq 0\)
**Step 2:** Two-tailed,
**Step 3:** Select significant level, \(\alpha\)
**Step 4:** Z test
**Step 5:** Find the critical value and determine if \(Z_{obt}\) is in the "reject" or "fail to reject" region.
Draw and label the graph.
**Graph Explanation:**
The graph illustrates a normal distribution curve. The middle section represents the "Fail to Reject" area, and the areas on both tails represent the "Reject" regions. The critical values \(Z_{crit}\) are marked on either side of the mean (\(\mu\)), dividing the total area into regions based on the selected significance level \(\alpha\).
Label the following:
\(*\alpha = 1 - \text{Confidence Level}, \alpha/2 = \text{area of each tail}\)*
\(*Z_{crit} \text{ Table}*\)
| Confidence Level (CL) | \(\alpha = 1 - \text{CL}\) | \(Z_{crit}\) |
|-----------------------|---------------------------|---------------|
| 90% (0.90) | \(1 - 0.90 = 0.10\) | \(\pm 1.645\) |
| 95% (0.95) | [Blank] | \(\pm 1.960\) |
| 99% (0.99) | | \(\pm 2.576\) |
**Step 6:** Calculate the Test statistics (\(Z_{obt}\))
- \(N =\) [Blank]
- \(\mu =\) [Blank]
- \(\sigma =\) [Blank]
- \(\overline{X} =\) [Blank]
Calculate:
\[Z_{obt} = \frac{\overline{X}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb16d438a-6747-410f-961a-8af2d5e6e1f5%2F480706a4-7de5-4f3f-9e0a-548091286600%2Fdsnim88_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here's a transcription of the text along with a detailed explanation of the graph for educational purposes.
---
**Steps in a Z Test**
**Step 1:** Determine the Null and Alternative Hypothesis
- \(H_0: \mu = \) [Blank] or \(M_1 - M_2 = 0\)
- \(H_a: \mu \neq \) [Blank] or \(M_1 - M_2 \neq 0\)
**Step 2:** Two-tailed,
**Step 3:** Select significant level, \(\alpha\)
**Step 4:** Z test
**Step 5:** Find the critical value and determine if \(Z_{obt}\) is in the "reject" or "fail to reject" region.
Draw and label the graph.
**Graph Explanation:**
The graph illustrates a normal distribution curve. The middle section represents the "Fail to Reject" area, and the areas on both tails represent the "Reject" regions. The critical values \(Z_{crit}\) are marked on either side of the mean (\(\mu\)), dividing the total area into regions based on the selected significance level \(\alpha\).
Label the following:
\(*\alpha = 1 - \text{Confidence Level}, \alpha/2 = \text{area of each tail}\)*
\(*Z_{crit} \text{ Table}*\)
| Confidence Level (CL) | \(\alpha = 1 - \text{CL}\) | \(Z_{crit}\) |
|-----------------------|---------------------------|---------------|
| 90% (0.90) | \(1 - 0.90 = 0.10\) | \(\pm 1.645\) |
| 95% (0.95) | [Blank] | \(\pm 1.960\) |
| 99% (0.99) | | \(\pm 2.576\) |
**Step 6:** Calculate the Test statistics (\(Z_{obt}\))
- \(N =\) [Blank]
- \(\mu =\) [Blank]
- \(\sigma =\) [Blank]
- \(\overline{X} =\) [Blank]
Calculate:
\[Z_{obt} = \frac{\overline{X}
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