Additional information: Difficult groups variance: 74.622 Easy groups variance: 25.111 1.) Write a conclusion about the effects of the different instructions, include the following: An explanation of the obtained value of the t
Additional information: Difficult groups variance: 74.622 Easy groups variance: 25.111 1.) Write a conclusion about the effects of the different instructions, include the following: An explanation of the obtained value of the t
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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Additional information:
Difficult groups variance: 74.622
Easy groups variance: 25.111
1.) Write a conclusion about the effects of the different instructions, include the following:
An explanation of the obtained value of the t-test.
Provide a measure of explained variance, and an explanation of it. .
Provide the effect size calculation, and explain the size of the effect.
The 95% confidence interval and its explanation.
Was the homogeneity of variance assumption “violated?” How do you know?
![**T-Test Analysis Explanation**
**Introduction:**
This analysis involves a T-Test conducted using a dataset named "DataSet1" to evaluate the differences between two groups based on a variable called "score". The dataset groups are labeled as "group(1 2)" and the analysis is concerned with missing values for the given variable.
**Group Statistics:**
The table below provides descriptive statistics for each group's scores based on their difficulty level:
| Difficulty | N | Mean | Std. Deviation | Std. Error Mean |
|------------|----|-------|----------------|-----------------|
| Difficult | 10 | 15.80 | 8.63842 | 2.73171 |
| 2.00 | 10 | 9.00 | 5.01110 | 1.58465 |
**Interpretation:**
- **N:** Number of samples in each group (10 for both).
- **Mean:** Average score for each group (15.80 for the difficult group and 9.00 for the 2.00 group).
- **Standard Deviation:** Variability of scores within each group (8.63842 for the difficult group and 5.01110 for the 2.00 group).
- **Standard Error Mean:** Estimated standard deviation of the sample mean (2.73171 for the difficult group and 1.58465 for the 2.00 group).
**Independent Samples Test:**
This part involves testing the hypothesis regarding the equality of means for the two groups.
**Levene's Test for Equality of Variances:**
- **F:** 7.401
- **Sig:** 0.014
- A significant value (< 0.05) suggests that the variances between groups are not equal.
**T-test Results:**
Used to determine if there is a significant difference between the means of two groups:
1. **Equal Variances Assumed:**
- **t:** 2.153
- **df:** 18
- **Sig (2-tailed):** 0.045
- **Mean Difference:** 6.80000
- **Standard Error Difference:** 3.15806
- **95% Confidence Interval:** [0.16517, 13.43483]
2. **Equal Variances Not Assumed:**
- **t:** 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c72e2d2-b0c3-42ae-9b81-186a94a5ff6a%2Fe8bf8e64-5b72-4339-ac1f-3e7dd2abe947%2Fg0eucl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**T-Test Analysis Explanation**
**Introduction:**
This analysis involves a T-Test conducted using a dataset named "DataSet1" to evaluate the differences between two groups based on a variable called "score". The dataset groups are labeled as "group(1 2)" and the analysis is concerned with missing values for the given variable.
**Group Statistics:**
The table below provides descriptive statistics for each group's scores based on their difficulty level:
| Difficulty | N | Mean | Std. Deviation | Std. Error Mean |
|------------|----|-------|----------------|-----------------|
| Difficult | 10 | 15.80 | 8.63842 | 2.73171 |
| 2.00 | 10 | 9.00 | 5.01110 | 1.58465 |
**Interpretation:**
- **N:** Number of samples in each group (10 for both).
- **Mean:** Average score for each group (15.80 for the difficult group and 9.00 for the 2.00 group).
- **Standard Deviation:** Variability of scores within each group (8.63842 for the difficult group and 5.01110 for the 2.00 group).
- **Standard Error Mean:** Estimated standard deviation of the sample mean (2.73171 for the difficult group and 1.58465 for the 2.00 group).
**Independent Samples Test:**
This part involves testing the hypothesis regarding the equality of means for the two groups.
**Levene's Test for Equality of Variances:**
- **F:** 7.401
- **Sig:** 0.014
- A significant value (< 0.05) suggests that the variances between groups are not equal.
**T-test Results:**
Used to determine if there is a significant difference between the means of two groups:
1. **Equal Variances Assumed:**
- **t:** 2.153
- **df:** 18
- **Sig (2-tailed):** 0.045
- **Mean Difference:** 6.80000
- **Standard Error Difference:** 3.15806
- **95% Confidence Interval:** [0.16517, 13.43483]
2. **Equal Variances Not Assumed:**
- **t:** 2
Transcribed Image Text:A psychologist aims to determine the impact of instructions on the time taken to solve a mechanical puzzle. Twenty volunteers are each given the same puzzle to solve as quickly as possible. Prior to the task, participants are randomly divided into two groups, each receiving different instructions. One group is told that the task is difficult, while the other is informed that it is easy. The score for each participant is the time, in minutes, taken to solve the puzzle. The research uses a two-tailed test with a significance level of α = 0.05.
**Data:**
- **Difficult Instruction:**
- Times (minutes): 5, 20, 7, 23, 30, 24, 9, 8, 20, 12
- **Easy Instruction:**
- Times (minutes): 13, 6, 6, 5, 3, 6, 10, 20, 9, 12
This setup is designed to examine the influence of perceived task difficulty on problem-solving efficiency.
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