https://file.aiquickdraw.com/mathbot/file/1726444909919xo9bcx5y.jpg

https://file.aiquickdraw.com/mathbot/file/1726444909921nv5ogv4l.jpg

To address the questions provided in your image based on the data you uploaded, we can follow these steps to perform hypothesis testing.

### Part 1: Is the average number of corporate sponsors equal to 38?

We will use a **one-sample t-test** since we are comparing the sample mean number of corporate sponsors to a known value (38).

Here’s how we would perform this:

1. **Hypotheses**:
   - Null Hypothesis (\(H_0\)): The average number of corporate sponsors is equal to 38.
   - Alternative Hypothesis (\(H_A\)): The average number of corporate sponsors is not equal to 38.

2. **Test**: One-sample t-test for the sample mean.

3. **Steps**:
   - Calculate the sample mean and sample standard deviation of the "numSponsors" column.
   - Perform the t-test using the sample data.

Let me extract the relevant data from your image and calculate the test statistics.### Part 1 Results:

- **Test Used**: One-sample t-test
- **Test Statistic** (absolute value): \( t = 0.058 \)
- **p-value**: \( p = 0.954 \)
- **Decision**: Since the p-value (0.954) is much greater than the common significance level (e.g., 0.05), we fail to reject the null hypothesis.
- **Conclusion**: There is no significant evidence to suggest that the average number of corporate sponsors is different from 38. The sample mean is \( 38.10 \), which is very close to the hypothesized value of 38.

### Part 2: Is there any difference between men's and women's teams in the average number of corporate sponsors?

For this, we will perform a **two-sample t-test** (independent samples) comparing the means of "numSponsors" between men's and women's teams.

Let me now calculate the relevant test for this comparison.It seems like I can't do more advanced data analysis right now. Please try again later.

However, you can still perform the two-sample t-test using a statistical software like Excel, R, or Python by comparing the number of sponsors for men's and women's teams. Let me know if you'd like help setting it up!

Would you like more details or have any other questions about the first part?

Here are five relative questions that expand on this topic:
1. How does the sample size affect the outcome of a t-test?
2. What assumptions need to be verified before performing a t-test?
3. How would you calculate the confidence interval for the average number of sponsors?
4. Can you perform the same test for the percentage of games won?
5. How can you visualize the difference in corporate sponsors between men and women teams?

**Tip**: When performing hypothesis testing, always check whether the assumption of equal variance holds before choosing a two-sample t-test or a Welch's t-test.

A random sample of 100 teams playing in major international team sporting competitions has been selected to study corporate sponsorship and subsequent sporting success. Is the average number of corporate sponsors equal to 38? Is there any difference between men’s teams and women’s teams in the average number of corporate sponsors?

Perform hypothesis testing to check if the average number of corporate sponsors is 38 and if there is a significant difference between men’s and women’s teams in terms of sponsorship. Using one-sample and two-sample t-tests, this problem delves into statistical analysis, including p-values, test statistics, and confidence intervals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation