**Independent Samples T-Test #1****Group Statistics:**- **Gender:** - *Male:* - N = 23 - Mean = 71.222 - Standard Deviation = 14.1632 - Standard Error Mean = 2.9532 - *Female:* - N = 23 - Mean = 78.983 - Standard Deviation = 12.2024 - Standard Error Mean = 2.5444**Independent Samples Test:**- **Levene's Test for Equality of Variances:** - F = 0.517 - Sig. (Significance) = 0.476- **t-test for Equality of Means:** - *Equal variances assumed:* - t = -1.991 - df (degrees of freedom) = 44 - Sig. (2-tailed) = 0.053 - Mean Difference = -7.7609 - Standard Error Difference = 3.8981 - 95% Confidence Interval of the Difference: Lower = -15.6171, Upper = 0.0953 - *Equal variances not assumed:* - t = -1.991 - df = 43.058 - Sig. (2-tailed) = 0.053 - Mean Difference = -7.7609 - Standard Error Difference = 3.8981 - 95% Confidence Interval of the Difference: Lower = -15.6219, Upper = 0.1002**Question 9:**Approximately what is the actual standardized effect size, d, for the mean differences between genders? (Use the average standard deviations for the groups in place of the pooled standard deviation.) **Understanding Confidence Intervals for Statistical Analysis**In statistical analysis, confidence intervals are crucial for estimating a population parameter based on sample data. This section explores the concept using a practical example.**Example Problem**Consider the following statement:"The 95% confidence interval for the mean FOR MALES (using the appropriate t critical value to 3 decimal places) for the variable FINAL EXAM % is..."**Explanation**This sentence is setting up a statistical problem to determine a confidence interval. Here’s a step-by-step explanation:1. **95% Confidence Interval**: This interval suggests that we are 95% confident that the true population mean falls within this range. The remaining 5% accounts for the possibility of the interval not capturing the mean due to sample variability.2. **Mean FOR MALES**: The analysis focuses specifically on male participants. The goal is to find the mean percentage score on a final exam for this group.3. **t Critical Value**: Since the sample size is likely limited or the population variance is unknown, the t-distribution is used over the z-distribution. The t critical value helps determine the margin of error and hence the width of the confidence interval.4. **FINAL EXAM %**: This variable measures the final exam scores expressed as a percentage. **Steps to Calculate the Confidence Interval:**1. **Calculate the Sample Mean ($\bar{x}$)**: Gather the final exam scores for males and compute the average.2. **Determine the Standard Deviation (s)**: Calculate how much individual scores deviate from the sample mean.3. **Find the Sample Size (n)**: Count the number of male participants included in the sample.4. **Calculate the Standard Error (SE)**: \[ SE = \frac{s}{\sqrt{n}} \]5. **Determine the t Critical Value (t\*)**: Refer to a t-distribution table using appropriate degrees of freedom ($df = n - 1$) and confidence level (95%).6. **Compute the Margin of Error (ME)**: \[ ME = t\* \times SE \]7. **Construct the Confidence Interval**: \[ \text{Confidence Interval} = \bar{x} \pm ME \]By following these steps, researchers can infer the likely range of the true mean final exam percentage for male students with 95% confidence.

Name: **Independent Samples T-Test #1****Group Statistics:**- **Gender:**
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Description: **Independent Samples T-Test #1****Group Statistics:**- **Gender:** - *Male:* - N = 23 - Mean = 71.222 - Standard Deviation = 14.1632 - Standard Error Mean = 2.9532 - *Female:* - N = 23 - Mean = 78.983 - Standard Deviation

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9. Approximately what is the actual standardized effect size, d, for the mean differences between genders? (use the average standard deviations for the groups in place of the pooled standard deviation)

9. Approximately what is the actual standardized effect size, d, for the mean differences between genders? (use the average standard deviations for the groups in place of the pooled standard deviation)

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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Topic Video

Question

**Independent Samples T-Test #1**

**Group Statistics:**

- **Gender:**
- *Male:*
- N = 23
- Mean = 71.222
- Standard Deviation = 14.1632
- Standard Error Mean = 2.9532
- *Female:*
- N = 23
- Mean = 78.983
- Standard Deviation = 12.2024
- Standard Error Mean = 2.5444

**Independent Samples Test:**

- **Levene's Test for Equality of Variances:**
- F = 0.517
- Sig. (Significance) = 0.476

- **t-test for Equality of Means:**
- *Equal variances assumed:*
- t = -1.991
- df (degrees of freedom) = 44
- Sig. (2-tailed) = 0.053
- Mean Difference = -7.7609
- Standard Error Difference = 3.8981
- 95% Confidence Interval of the Difference: Lower = -15.6171, Upper = 0.0953

- *Equal variances not assumed:*
- t = -1.991
- df = 43.058
- Sig. (2-tailed) = 0.053
- Mean Difference = -7.7609
- Standard Error Difference = 3.8981
- 95% Confidence Interval of the Difference: Lower = -15.6219, Upper = 0.1002

**Question 9:**

Approximately what is the actual standardized effect size, d, for the mean differences between genders? (Use the average standard deviations for the groups in place of the pooled standard deviation.)

**Understanding Confidence Intervals for Statistical Analysis**

In statistical analysis, confidence intervals are crucial for estimating a population parameter based on sample data. This section explores the concept using a practical example.

**Example Problem**

Consider the following statement:

"The 95% confidence interval for the mean FOR MALES (using the appropriate t critical value to 3 decimal places) for the variable FINAL EXAM % is..."

**Explanation**

This sentence is setting up a statistical problem to determine a confidence interval. Here’s a step-by-step explanation:

1. **95% Confidence Interval**: This interval suggests that we are 95% confident that the true population mean falls within this range. The remaining 5% accounts for the possibility of the interval not capturing the mean due to sample variability.

2. **Mean FOR MALES**: The analysis focuses specifically on male participants. The goal is to find the mean percentage score on a final exam for this group.

3. **t Critical Value**: Since the sample size is likely limited or the population variance is unknown, the t-distribution is used over the z-distribution. The t critical value helps determine the margin of error and hence the width of the confidence interval.

4. **FINAL EXAM %**: This variable measures the final exam scores expressed as a percentage.

**Steps to Calculate the Confidence Interval:**

1. **Calculate the Sample Mean ($\bar{x}$)**: Gather the final exam scores for males and compute the average.

2. **Determine the Standard Deviation (s)**: Calculate how much individual scores deviate from the sample mean.

3. **Find the Sample Size (n)**: Count the number of male participants included in the sample.

4. **Calculate the Standard Error (SE)**: \[ SE = \frac{s}{\sqrt{n}} \]

5. **Determine the t Critical Value (t\*)**: Refer to a t-distribution table using appropriate degrees of freedom ($df = n - 1$) and confidence level (95%).

6. **Compute the Margin of Error (ME)**: \[ ME = t\* \times SE \]

7. **Construct the Confidence Interval**:
\[ \text{Confidence Interval} = \bar{x} \pm ME \]

By following these steps, researchers can infer the likely range of the true mean final exam percentage for male students with 95% confidence.

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