A random sample of 105 teams playing in major international team sporting competitions has been selected to study corporate sponsorship and subsequent sporting success. Some of the variables recorded for each team are listed below.

Variable	Description
subid	Subject ID
sex	sex of players
numSponsors	number of distinct corporate sponsors
percentWin	the percentage of international games won
Address the following questions, assuming as necessary that all test assumptions are verified.
Part 1
A test is run to answer the research question, ’Is there any difference between men’s teams and women’s teams in the average number of corporate sponsors?’
Which test is correct to use, if we do not know the population standard deviation?	Answer 1 Question 1
 
What is the null hypothesis?	Answer 2 Question 1
 
The p-value of the test is 0.312. What is the decision of the test?

**Answer 1 Question 1**  
Since we are comparing the means of two independent groups (men's and women's teams) and we do not know the population standard deviation, the appropriate test to use is the **independent samples t-test** (also known as a two-sample t-test). This test is commonly used when the variances are unknown, and we can assume normal distribution of the data.

**Answer 2 Question 1**  
The null hypothesis (\( H_0 \)) for this test would be:

\[
H_0: \mu_{men} = \mu_{women}
\]

This means that there is no significant difference between the average number of corporate sponsors for men’s and women’s teams.

**Decision based on p-value**  
The p-value of 0.312 is higher than the commonly used significance level (\(\alpha = 0.05\)).

Since \( p = 0.312 > 0.05 \), we **fail to reject the null hypothesis**. This means that there is no statistically significant evidence to suggest that the average number of corporate sponsors differs between men’s and women’s teams.

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Do you want further details on how the t-test works, or have any questions?

Here are 5 related questions to expand on the above:

1. What assumptions must be satisfied for an independent samples t-test to be valid?
2. How would you interpret the result if the p-value had been less than 0.05?
3. What could we do if the assumption of equal variances between groups is violated?
4. How can sample size impact the reliability of this t-test?
5. What alternative tests could be used if the normality assumption is violated?

**Tip:** When conducting hypothesis tests, always check whether assumptions like normality and equal variances hold to ensure valid conclusions.

A random sample of 105 teams playing in major international team sporting competitions has been selected to study corporate sponsorship and subsequent sporting success. Some of the variables recorded for each team are listed below. 
Variable Description: 
subid - Subject ID 
sex - sex of players 
numSponsors - number of distinct corporate sponsors 
percentWin - the percentage of international games won. 
Address the following questions, assuming as necessary that all test assumptions are verified. 
Part 1: A test is run to answer the research question, 'Is there any difference between men’s teams and women’s teams in the average number of corporate sponsors?' Which test is correct to use, if we do not know the population standard deviation? 
What is the null hypothesis? 
The p-value of the test is 0.312. What is the decision of the test?

This problem explores hypothesis testing for corporate sponsorship in men's and women's teams, using an independent samples t-test. The question examines whether there is a significant difference in the average number of sponsors between genders, with a p-value of 0.312. Learn the key concepts of hypothesis testing, t-tests, and p-values in this example.

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