Help ### Hypothesis Testing Decision Process#### Step 1: Compare the p-value to the significance level (α)The p-value is...- ○ less than (or equal to) α- ○ greater than α#### Step 2: Decision RuleThis test statistic leads to a decision to...- ○ reject the null- ○ accept the null- ○ fail to reject the null#### Step 3: Final ConclusionAs such, the final conclusion is that...- ○ There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.- ○ There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.- ○ The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0.- ○ There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.### Explanation:In hypothesis testing, you determine whether to reject the null hypothesis (which typically represents no effect or no difference) based on your p-value and your chosen significance level (α). Here's how you approach it:1. **Compare the p-value to α**: Determine if your p-value is less than or equal to α (e.g., 0.05, 0.01). If so, it suggests that the observed data is unlikely under the null hypothesis.2. **Decision Rule**: Based on the comparison: - If the p-value is less than or equal to α, you reject the null hypothesis. - If the p-value is greater than α, you fail to reject the null hypothesis.3. **Final Conclusion**: Draw a conclusion based on your decision rule: - Rejection implies there is significant evidence to support the alternative hypothesis. - Failing to reject implies there isn't enough evidence to support the alternative hypothesis. ### Hypothesis Testing for Difference in Pre-Test and Post-Test Scores#### Problem StatementYou wish to test the following claim ($H_a$) at a significance level of $\alpha = 0.10$. For the context of this problem, $\mu_d = PostTest - PreTest$. One data set represents a pre-test and the other data set represents a post-test. Each row represents the pre and post-test scores for an individual.\[\begin{aligned}H_0: \mu_d &= 0 \\H_a: \mu_d &\ne 0\end{aligned}\]#### Data CollectionYou believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:| pre-test | post-test ||----------|------------|| 31.4 | 36.2 || 56.4 | 43 || 55.1 | 45 || 75.1 | 81 || 34.4 | 42.1 || 60.1 | 79.5 || 50.6 | 56.3 || 62.8 | 62.9 || 34.4 | 55.8 || 54.2 | 58.6 || 66.7 | 69.6 || 57 | 49.9 || 43.5 | 49.2 || 64.8 | 56.5 || 44.1 | 35.8 || 69.4 | 80.3 || 56.4 | 58.3 |#### Statistical Calculation1. **Difference Calculation**: For each individual, calculate the difference between the post-test score and the pre-test score.2. **Mean Difference ($\bar{d}$)**: Compute the average of these differences.3. **Standard Deviation of Differences (s\_d)**: Compute the standard deviation of these differences.4. **Test Statistic ($t$)**: Calculate the test statistic using the formula: \[ t = \frac{\bar{d} - \mu_d

Name: Help ### Hypothesis Testing Decision Process#### Step 1: Compare the p
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: Help ### Hypothesis Testing Decision Process#### Step 1: Compare the p-value to the significance level (α)The p-value is...- ○ less than (or equal to) α- ○ greater than α#### Step 2: Decision RuleThis test statistic leads to a decision to...- ○ rejec

1. test statistics = -1.0833 2. P- value = 0.294733 ~0.2947 3. P value is greater than alpha 4.…

Answered: The p-value is... O less than (or equal…

Math

Statistics

The p-value is... O less than (or equal to) a greater than a This test statistic leads to a decision to... O reject the null accept the null fail to reject the null

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: 1) Determine the recursive and explicit Cath term) defmitions for Hthe following sequences: a)…

Q: I need help

Q: help with this

Q: Help break down

A: We have to find mean and stanadard deviation..

Q: image

Q: help ?

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

100%

Help

### Hypothesis Testing Decision Process

#### Step 1: Compare the p-value to the significance level (α)
The p-value is...
- ○ less than (or equal to) α
- ○ greater than α

#### Step 2: Decision Rule
This test statistic leads to a decision to...
- ○ reject the null
- ○ accept the null
- ○ fail to reject the null

#### Step 3: Final Conclusion
As such, the final conclusion is that...
- ○ There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
- ○ There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
- ○ The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0.
- ○ There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.

### Explanation:
In hypothesis testing, you determine whether to reject the null hypothesis (which typically represents no effect or no difference) based on your p-value and your chosen significance level (α). Here's how you approach it:

1. **Compare the p-value to α**: Determine if your p-value is less than or equal to α (e.g., 0.05, 0.01). If so, it suggests that the observed data is unlikely under the null hypothesis.
2. **Decision Rule**: Based on the comparison:
- If the p-value is less than or equal to α, you reject the null hypothesis.
- If the p-value is greater than α, you fail to reject the null hypothesis.
3. **Final Conclusion**: Draw a conclusion based on your decision rule:
- Rejection implies there is significant evidence to support the alternative hypothesis.
- Failing to reject implies there isn't enough evidence to support the alternative hypothesis.

### Hypothesis Testing for Difference in Pre-Test and Post-Test Scores

#### Problem Statement
You wish to test the following claim ($H_a$) at a significance level of $\alpha = 0.10$. For the context of this problem, $\mu_d = PostTest - PreTest$. One data set represents a pre-test and the other data set represents a post-test. Each row represents the pre and post-test scores for an individual.

\[
\begin{aligned}
H_0: \mu_d &= 0 \\
H_a: \mu_d &\ne 0
\end{aligned}
\]

#### Data Collection
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

| pre-test | post-test |
|----------|------------|
| 31.4 | 36.2 |
| 56.4 | 43 |
| 55.1 | 45 |
| 75.1 | 81 |
| 34.4 | 42.1 |
| 60.1 | 79.5 |
| 50.6 | 56.3 |
| 62.8 | 62.9 |
| 34.4 | 55.8 |
| 54.2 | 58.6 |
| 66.7 | 69.6 |
| 57 | 49.9 |
| 43.5 | 49.2 |
| 64.8 | 56.5 |
| 44.1 | 35.8 |
| 69.4 | 80.3 |
| 56.4 | 58.3 |

#### Statistical Calculation

1. **Difference Calculation**: For each individual, calculate the difference between the post-test score and the pre-test score.
2. **Mean Difference ($\bar{d}$)**: Compute the average of these differences.
3. **Standard Deviation of Differences (s\_d)**: Compute the standard deviation of these differences.
4. **Test Statistic ($t$)**: Calculate the test statistic using the formula:

\[
t = \frac{\bar{d} - \mu_d

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Summary

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions