4. Professor Dumbledore wanted to know whether students in Gryffindor house were performing better than students in Slytherin house. He asked Professors Snape and Slughorn to provide their scores in Defense Against the Dark Arts and Potions for comparison. The information he received was as follows:

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I need these two questions answered please!

 

Certainly! Here's a transcription and explanation of the document for use on an educational website:

---

**Psy 213: Statistical Analysis in Education**

**4. Comparing Academic Performance Between Hogwarts Houses**

Professor Dumbledore wanted to evaluate whether students in Gryffindor house perform better academically than students in Slytherin house. For this analysis, he requested Professors Snape and Slughorn to provide the student scores in two subjects: Defense Against the Dark Arts and Potions. The results obtained are outlined below:

**Potions:**

- **Slytherin:**
  - Sample size (n) = 18
  - Variance (s²) = 14.33
  - Mean = 71.22

- **Gryffindor:**
  - Sample size (n) = 20
  - Variance (s²) = 12.22
  - Mean = 85.77

**Defense Against the Dark Arts:**

- **Slytherin:**
  - Sample size (n) = 18
  - Variance (s²) = 10.13
  - Mean = 90.45

- **Gryffindor:**
  - Sample size (n) = 20
  - Variance (s²) = 12.76
  - Mean = 81.22

**Tasks:**
a. Calculate the independent samples t-test for both the Potions class and Defense Against the Dark Arts class.

b. Determine if the null hypothesis can be rejected (i.e., if there is a statistically significant difference in performance between Slytherin and Gryffindor).

**Explanation:**

The table presents a comparison of student scores from two different Hogwarts houses in two subjects. For each house and subject, the table includes the sample size (number of students), variance (a measure of score distribution), and the mean score (average performance).

The task at hand involves using these statistics to conduct independent samples t-tests. This statistical method will help determine if there is a significant difference in academic performance between the two houses for each subject. Rejecting the null hypothesis would imply a significant performance difference, while failure to reject indicates no significant difference.

---

This text is designed to engage students by incorporating familiar fictional elements while teaching statistical concepts.
Transcribed Image Text:Certainly! Here's a transcription and explanation of the document for use on an educational website: --- **Psy 213: Statistical Analysis in Education** **4. Comparing Academic Performance Between Hogwarts Houses** Professor Dumbledore wanted to evaluate whether students in Gryffindor house perform better academically than students in Slytherin house. For this analysis, he requested Professors Snape and Slughorn to provide the student scores in two subjects: Defense Against the Dark Arts and Potions. The results obtained are outlined below: **Potions:** - **Slytherin:** - Sample size (n) = 18 - Variance (s²) = 14.33 - Mean = 71.22 - **Gryffindor:** - Sample size (n) = 20 - Variance (s²) = 12.22 - Mean = 85.77 **Defense Against the Dark Arts:** - **Slytherin:** - Sample size (n) = 18 - Variance (s²) = 10.13 - Mean = 90.45 - **Gryffindor:** - Sample size (n) = 20 - Variance (s²) = 12.76 - Mean = 81.22 **Tasks:** a. Calculate the independent samples t-test for both the Potions class and Defense Against the Dark Arts class. b. Determine if the null hypothesis can be rejected (i.e., if there is a statistically significant difference in performance between Slytherin and Gryffindor). **Explanation:** The table presents a comparison of student scores from two different Hogwarts houses in two subjects. For each house and subject, the table includes the sample size (number of students), variance (a measure of score distribution), and the mean score (average performance). The task at hand involves using these statistics to conduct independent samples t-tests. This statistical method will help determine if there is a significant difference in academic performance between the two houses for each subject. Rejecting the null hypothesis would imply a significant performance difference, while failure to reject indicates no significant difference. --- This text is designed to engage students by incorporating familiar fictional elements while teaching statistical concepts.
**Topic: Analyzing Alcohol Consumption by Gender Using an Independent-Samples T-Test**

In this study, we aim to explore whether there is a significant difference between men and women in terms of alcohol consumption on a typical week. An independent-samples t-test is conducted using the data provided for males and females, with sample sizes of \( n=5 \) each. The variable of interest is "alc.week," representing weekly alcohol intake.

**Data Table:**

| Males | Females |
|-------|---------|
| 10    | 15      |
| 4     | 3       |
| 0     | 4       |
| 7     | 0       |
| 17    | 2       |

**Descriptive Statistics:**

- **Variance:**
  - Males: \( S^2_{\text{males}} = 41.30 \)
  - Females: \( S^2_{\text{females}} = 34.70 \)

- **Means:**
  - Males: Mean = 7.6
  - Females: Mean = 4.8

The study seeks to determine if these differences in mean weekly alcohol consumption are statistically significant. The t-test will help in assessing the variance and means to conclude whether the observed differences can be attributed to gender differences or are due to random chance.
Transcribed Image Text:**Topic: Analyzing Alcohol Consumption by Gender Using an Independent-Samples T-Test** In this study, we aim to explore whether there is a significant difference between men and women in terms of alcohol consumption on a typical week. An independent-samples t-test is conducted using the data provided for males and females, with sample sizes of \( n=5 \) each. The variable of interest is "alc.week," representing weekly alcohol intake. **Data Table:** | Males | Females | |-------|---------| | 10 | 15 | | 4 | 3 | | 0 | 4 | | 7 | 0 | | 17 | 2 | **Descriptive Statistics:** - **Variance:** - Males: \( S^2_{\text{males}} = 41.30 \) - Females: \( S^2_{\text{females}} = 34.70 \) - **Means:** - Males: Mean = 7.6 - Females: Mean = 4.8 The study seeks to determine if these differences in mean weekly alcohol consumption are statistically significant. The t-test will help in assessing the variance and means to conclude whether the observed differences can be attributed to gender differences or are due to random chance.
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