https://file.aiquickdraw.com/mathbot/file/1726102915547pnls7lbc.csv

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The task involves analyzing data from a study on non-verbal communication among married or de facto couples in the Sydney region. The main objectives are:

1. **Part 1**: Determine if there is a difference between men and women in the average relationship length.
2. **Part 2**: Assess if the average relationship length is equal to 38 years.

I'll guide you through the steps required to answer these questions using the provided data.

**Steps to Approach:**

### Part 1: Comparing Average Relationship Lengths between Men and Women

**Hypothesis Test:**
- **Null Hypothesis (H₀):** There is no difference in the average relationship length between men and women.
- **Alternative Hypothesis (H₁):** There is a difference in the average relationship length between men and women.

**Test Type:**
- Use a **two-sample t-test** (independent samples) since you're comparing two means (men vs. women).

### Part 2: Testing if Average Relationship Length Equals 38 Years

**Hypothesis Test:**
- **Null Hypothesis (H₀):** The average relationship length is 38 years.
- **Alternative Hypothesis (H₁):** The average relationship length is not 38 years.

**Test Type:**
- Use a **one-sample t-test** comparing the sample mean to 38.

To proceed, I'll:
1. Load and analyze the data from the CSV file you provided.
2. Perform the necessary statistical tests and provide the results, including test statistics, p-values, and conclusions.

Let's begin by loading and examining the data in the CSV file.The dataset contains the following columns:
- **SubID**: Subject ID
- **sex**: Sex of the guesser (male or female)
- **years**: Length of the relationship in years
- **percentage**: The percentage of correct guesses in the non-verbal communication task

### Part 1: Difference in Average Relationship Length between Men and Women

I'll perform a two-sample t-test to compare the average relationship lengths between men and women.

### Part 2: Testing if the Average Relationship Length Equals 38 Years

I'll perform a one-sample t-test to test if the overall average relationship length is 38 years.

Let's perform these tests and calculate the required statistics.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can perform these tests manually or with software like Excel, R, or Python using the steps below:

### Steps to Perform the Tests:

**Part 1: Two-Sample t-test for Average Relationship Length Between Men and Women**
1. **Hypothesis Setup**:
   - Null Hypothesis (H₀): There is no difference in the average relationship length between men and women.
   - Alternative Hypothesis (H₁): There is a difference in the average relationship length between men and women.
2. **Test Type**: Use a two-sample t-test (independent samples).
3. **Using Excel**: Use the `T.TEST` function to compare the two samples.
   
**Part 2: One-Sample t-test to Check if Average Relationship Length Equals 38 Years**
1. **Hypothesis Setup**:
   - Null Hypothesis (H₀): The average relationship length is 38 years.
   - Alternative Hypothesis (H₁): The average relationship length is not 38 years.
2. **Test Type**: Use a one-sample t-test.
3. **Using Excel**: Use the `T.TEST` function to compare the sample mean to 38.

### Let me know if you need further help or want to try something else! 

### Related Questions:
1. How do you interpret the p-value in hypothesis testing?
2. What assumptions must be met to use a two-sample t-test?
3. How can you use Excel to calculate the t-statistic manually?
4. What is the impact of sample size on hypothesis testing?
5. How does the t-distribution compare to the normal distribution?

### Tip:
Always check the assumptions of normality and equal variances when performing t-tests to ensure the validity of your results.

Is there any difference between men and women in the average relationship length? Is the average relationship length equal to 38?

Analyze relationship length differences between men and women using hypothesis testing. Learn to apply the Two-Sample and One-Sample t-tests, interpret p-values, and perform statistical tests for real-world scenarios.

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