Dear Expert, I need help. The pictures attached are the questions and below is the rest of the part. Thank you very much, t-critical= t= Fail to reject H₀. The mean difference is not significant. Reject H₀. The mean difference is not significant. Reject H₀. The mean difference is significant. Fail to reject H₀. The mean difference is significant. Now assume that the data are from a repeated-measures study using the same sample of n = 9 participants in both treatment conditions. Compute the variance for the sample of difference scores and the estimated standard error for the mean difference. (Hint: This time you should find that removing the individual differences does not reduce the variance or the standard error.)s²= sMDMD= Compute the repeated measures t statistic. Using α = .05, is there a significant difference between the two sets of scores?t-critical= t= Fail to reject H₀. The mean difference is not significant. Fail to reject H₀. The mean difference is significant. Reject H₀. The mean difference is significant. Reject H₀. The mean difference is not significant. ### Educational Content: Independent-Measures Study#### Data Input Section- **Sample 1 (M, SS):** - M = [Input Box] - SS = [Input Box]- **Sample 2 (M, SS):** - M = [Input Box] - SS = [Input Box]- **Combined Sample (M, SS):** - M = [Input Box] - SS = [Input Box]#### Task DescriptionAssume that the data are from an independent-measures study using two separate samples, each with n = 9 participants. Compute the pooled variance and the estimated standard error for the mean difference. (Use three decimal places.)- **Pooled Variance (\(s^2_p\)):** [Input Box]- **Estimated Standard Error (\(S_{M1 - M2}\)):** [Input Box]#### Statistical AnalysisCompute the independent measures t statistic. Using α = 0.05, determine if there is a significant difference between the two sets of scores.#### Graphical Representation**t Distribution Graph:**- **Degrees of Freedom:** 11A graph displays a t distribution curve, shaded in blue, centered at zero (0.0) on the x-axis, extending from approximately -3.0 to 3.0. The graph is interactive, with an adjustable slider to set degrees of freedom (currently set to 11).**Graph Selection Options:**- Three icons below offer different views of the distribution: - First icon: Standard view. - Second icon: Alternative view. - Third icon: Another visual option.These features aid in understanding the behavioral characteristics of the t distribution under different degrees of freedom. **Transcription for Educational Website**### Gravetter/Wallnau/Forzano, Essentials - Chapter 11 - End-of-chapter Question 21The previous problem demonstrates that removing individual differences can substantially reduce variance and lower the standard error. However, this benefit occurs only if the individual differences are consistent across treatment conditions. In the previous problem, for example, the participants with the highest scores in the neutral-word condition also had the highest scores in the swear-word condition. Similarly, participants with the lowest scores in the neutral-word condition also had the lowest scores in the swear-word condition. The following data consist of the scores in the previous problem, but with the scores in the swear-word condition scrambled to eliminate the consistency of the individual differences.Complete the following table and find \( M \) (mean) and \( SS \) (sum of squares) for each group of scores and for the differences.#### Table:| Participant | Neutral Word \( X_1 \) | Swearing \( X_2 \) | Difference \( D = X_2 - X_1 \) ||-------------|-------------------------|--------------------|-------------------------------|| A | 9 | 5 | || B | 9 | 2 | || C | 9 | 5 | || D | 4 | 10 | || E | 10 | 8 | || F | 9 | 4 | || G | 6 | 7 | || H | 10 | 5 | || I | 6 | 8 | |#### Summary:- \( \Sigma \) (sum) of each column- \( M = \) (mean) of each group- \( SS = \) (sum of squares) for each groupIn this exercise, you need to calculate the difference between the swearing and neutral word scores for each participant and compute the statistics \( M \) and \( SS \) for these data sets.

Given that Let X1 represent Neural Word and X2 denote the Swearing .... Data is given as paired…

Answered: The previous problem demonstrates that…

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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Dear Expert, I need help. The pictures attached are the questions and below is the rest of the part.

Thank you very much,

t-critical	=
t	=

Fail to reject H₀. The mean difference is not significant.

Reject H₀. The mean difference is not significant.

Reject H₀. The mean difference is significant.

Fail to reject H₀. The mean difference is significant.

Now assume that the data are from a repeated-measures study using the same sample of n = 9 participants in both treatment conditions. Compute the variance for the sample of difference scores and the estimated standard error for the mean difference. (Hint: This time you should find that removing the individual differences does not reduce the variance or the standard error.)

s²	=
sMDMD	=

Compute the repeated measures t statistic. Using α = .05, is there a significant difference between the two sets of scores?

t-critical	=
t	=

Fail to reject H₀. The mean difference is not significant.

Fail to reject H₀. The mean difference is significant.

Reject H₀. The mean difference is significant.

Reject H₀. The mean difference is not significant.

### Educational Content: Independent-Measures Study

#### Data Input Section
- **Sample 1 (M, SS):**
- M = [Input Box]
- SS = [Input Box]

- **Sample 2 (M, SS):**
- M = [Input Box]
- SS = [Input Box]

- **Combined Sample (M, SS):**
- M = [Input Box]
- SS = [Input Box]

#### Task Description
Assume that the data are from an independent-measures study using two separate samples, each with n = 9 participants. Compute the pooled variance and the estimated standard error for the mean difference. (Use three decimal places.)

- **Pooled Variance (\(s^2_p\)):** [Input Box]
- **Estimated Standard Error (\(S_{M1 - M2}\)):** [Input Box]

#### Statistical Analysis
Compute the independent measures t statistic. Using α = 0.05, determine if there is a significant difference between the two sets of scores.

#### Graphical Representation

**t Distribution Graph:**
- **Degrees of Freedom:** 11

A graph displays a t distribution curve, shaded in blue, centered at zero (0.0) on the x-axis, extending from approximately -3.0 to 3.0. The graph is interactive, with an adjustable slider to set degrees of freedom (currently set to 11).

**Graph Selection Options:**
- Three icons below offer different views of the distribution:
- First icon: Standard view.
- Second icon: Alternative view.
- Third icon: Another visual option.

These features aid in understanding the behavioral characteristics of the t distribution under different degrees of freedom.

**Transcription for Educational Website**

### Gravetter/Wallnau/Forzano, Essentials - Chapter 11 - End-of-chapter Question 21

The previous problem demonstrates that removing individual differences can substantially reduce variance and lower the standard error. However, this benefit occurs only if the individual differences are consistent across treatment conditions. In the previous problem, for example, the participants with the highest scores in the neutral-word condition also had the highest scores in the swear-word condition. Similarly, participants with the lowest scores in the neutral-word condition also had the lowest scores in the swear-word condition. The following data consist of the scores in the previous problem, but with the scores in the swear-word condition scrambled to eliminate the consistency of the individual differences.

Complete the following table and find \( M \) (mean) and \( SS \) (sum of squares) for each group of scores and for the differences.

#### Table:

| Participant | Neutral Word \( X_1 \) | Swearing \( X_2 \) | Difference \( D = X_2 - X_1 \) |
|-------------|-------------------------|--------------------|-------------------------------|
| A | 9 | 5 | |
| B | 9 | 2 | |
| C | 9 | 5 | |
| D | 4 | 10 | |
| E | 10 | 8 | |
| F | 9 | 4 | |
| G | 6 | 7 | |
| H | 10 | 5 | |
| I | 6 | 8 | |

#### Summary:

- \( \Sigma \) (sum) of each column
- \( M = \) (mean) of each group
- \( SS = \) (sum of squares) for each group

In this exercise, you need to calculate the difference between the swearing and neutral word scores for each participant and compute the statistics \( M \) and \( SS \) for these data sets.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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