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Can you please complete the chart and what are the t-criticals

Can you please complete the chart and what are the t-criticals

MATLAB: An Introduction with Applications
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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Can you please complete the chart and what are the t-criticals? 

 

### Statistical Analysis: Understanding t-Tests #### Hypothesis Testing 1. **t-critical**: \[ \text{t-critical} = \_\_\_ \] 2. **t-value**: \[ t = \textbf{1.85} \] #### Decision Rule Based on t-values: - ☑️ Fail to reject \( H_0 \). The mean difference is not significant. - ⬜ Reject \( H_0 \). The mean difference is not significant. - ⬜ Reject \( H_0 \). The mean difference is significant. - ⬜ Fail to reject \( H_0 \). The mean difference is significant. #### Repeated-Measures Study Assume 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: A repeated-measures design substantially reduces the variance and the standard error.)* - **Variance (\( s^2 \))**: \[ s^2 = \textbf{4.000} \] - **Estimated Standard Error (\( S_{MD} \))**: \[ S_{MD} = \textbf{0.667} \] #### Repeated Measures t-test: Compute the repeated measures t statistic. Using \( \alpha = .05 \), determine if there is a significant difference between the two sets of scores. 1. **t-critical**: \[ \text{t-critical} = \_\_\_ \] 2. **t-value**: \[ t = \textbf{-3.00} \]
Transcribed Image Text:### Statistical Analysis: Understanding t-Tests #### Hypothesis Testing 1. **t-critical**: \[ \text{t-critical} = \_\_\_ \] 2. **t-value**: \[ t = \textbf{1.85} \] #### Decision Rule Based on t-values: - ☑️ Fail to reject \( H_0 \). The mean difference is not significant. - ⬜ Reject \( H_0 \). The mean difference is not significant. - ⬜ Reject \( H_0 \). The mean difference is significant. - ⬜ Fail to reject \( H_0 \). The mean difference is significant. #### Repeated-Measures Study Assume 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: A repeated-measures design substantially reduces the variance and the standard error.)* - **Variance (\( s^2 \))**: \[ s^2 = \textbf{4.000} \] - **Estimated Standard Error (\( S_{MD} \))**: \[ S_{MD} = \textbf{0.667} \] #### Repeated Measures t-test: Compute the repeated measures t statistic. Using \( \alpha = .05 \), determine if there is a significant difference between the two sets of scores. 1. **t-critical**: \[ \text{t-critical} = \_\_\_ \] 2. **t-value**: \[ t = \textbf{-3.00} \]
Swearing is a common, almost reflexive, response to pain. Whether you knock your shin into the edge of a coffee table or smash your thumb with a hammer, most of us respond with a streak of obscenities. One question, however, is whether swearing has any effect on the amount of pain that you feel. To address this issue, Stephens, Atkins, and Kingston (2009) conducted an experiment comparing swearing with other responses to pain. In the study, participants were asked to place one hand in icy cold water for as long as they could bear the pain. Half of the participants were told to repeat their favorite swear word over and over for as long as their hands were in the water. The other half repeated a neutral word. The researchers recorded how long each participant was able to tolerate the ice water. After a brief rest, the two groups switched words and repeated the ice water plunge. Thus, all the participants experienced both conditions (swearing and neutral) with half swearing on their first plunge and half on their second. The data in the following table are representative of the results obtained in the study and represent the reports of pain level of n = 9 participants. Complete the following table and find M and SS for each group of scores and for the differences. | Participant | Neutral Word \(X_1\) | Swearing \(X_2\) | Difference \(D = X_2 - X_1\) | |-------------|----------------------|-----------------|-------------------------------| | A | 9 | 7 | | | B | 9 | 8 | | | C | 9 | 5 | | | D | 4 | 5 | | | E | 10 | 8 | | | F | 9 | 4 | | | G | 6 | 5 | | | H | 10 | 10 | | | I | 6 | 2 | | | | Σ | | | | | M = | M = | M = | | | SS = | SS = | SS = |
Transcribed Image Text:Swearing is a common, almost reflexive, response to pain. Whether you knock your shin into the edge of a coffee table or smash your thumb with a hammer, most of us respond with a streak of obscenities. One question, however, is whether swearing has any effect on the amount of pain that you feel. To address this issue, Stephens, Atkins, and Kingston (2009) conducted an experiment comparing swearing with other responses to pain. In the study, participants were asked to place one hand in icy cold water for as long as they could bear the pain. Half of the participants were told to repeat their favorite swear word over and over for as long as their hands were in the water. The other half repeated a neutral word. The researchers recorded how long each participant was able to tolerate the ice water. After a brief rest, the two groups switched words and repeated the ice water plunge. Thus, all the participants experienced both conditions (swearing and neutral) with half swearing on their first plunge and half on their second. The data in the following table are representative of the results obtained in the study and represent the reports of pain level of n = 9 participants. Complete the following table and find M and SS for each group of scores and for the differences. | Participant | Neutral Word \(X_1\) | Swearing \(X_2\) | Difference \(D = X_2 - X_1\) | |-------------|----------------------|-----------------|-------------------------------| | A | 9 | 7 | | | B | 9 | 8 | | | C | 9 | 5 | | | D | 4 | 5 | | | E | 10 | 8 | | | F | 9 | 4 | | | G | 6 | 5 | | | H | 10 | 10 | | | I | 6 | 2 | | | | Σ | | | | | M = | M = | M = | | | SS = | SS = | SS = |
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