Math Problem Statement

sample (10).csv

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A random sample of 146 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 numFollowersCat the number of followers of teams

Import the data set included in the file sample.csv in Excel. To do this, you need to click on the link above and save the data file in a convenient location on your PC (in your browser, File and Save). Next open Excel, click File in the Menu, select Open and navigate to the file you previously saved – or simply double-click on it, Excel should open automatically. Use Excel and/or probTool, and appropriate hypothesis tests, to address the following research question. Assume all the test assumptions are verified.

Research question 1: We wish to investigate whether the number of followers of teams playing in major international team sporting competitions is distributed according to the table below.

the number of followers of teams | 1 (10000 or less) | 2 (10001-50000) | 3 (50001-100000) | 4 (100001 or more) Percentage | 10 | 10 | 50 | 30 QUESTIONS:

Report the number of the degrees of freedom [integer]: Answer 1 Question 1 Report the value of the test statistic [use at least 2dp]: Answer 2 Question 1 Report the 𝑝 -value [use at least 3dp]: Answer 3 Question 1 What is the decision of the test? Answer 4 Question 1

Research question 2: we are interested in studying the association between the number of followers and the sex of players in the population under consideration. QUESTIONS:

Report the number of the degrees of freedom [integer]: Answer 5 Question 1 Report the value of the test statistic [use at least 2dp]: Answer 6 Question 1 Report the 𝑝 -value [use at least 3dp]: Answer 7 Question 1 What is the decision of the test? Answer 8 Question 1

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Solution

The dataset contains information about teams in major international sporting competitions, including the sex of players, the number of sponsors, win percentage, and follower categories. There is also a contingency table for follower categories and player sex.

Research Question 1:

To determine if the number of followers is distributed according to the specified percentages (10%, 10%, 50%, 30%), we will conduct a Chi-square goodness-of-fit test. The expected counts will be calculated based on the percentages provided.

Research Question 2:

For studying the association between the number of followers and player sex, we will use a Chi-square test of independence, utilizing the contingency table to analyze whether the distribution of followers differs by player sex.

Let me perform these calculations step by step.### Research Question 1 Results:

  1. Degrees of freedom: 3
  2. Chi-square test statistic: 55.32
  3. p-value: 0.000
  4. Decision: Since the p-value is much less than 0.05, we reject the null hypothesis, indicating that the distribution of followers does not match the specified percentages.

Now, let's proceed with Research Question 2 by performing a Chi-square test of independence using the contingency table provided.### Research Question 2 Results:

  1. Degrees of freedom: 3
  2. Chi-square test statistic: 1.98
  3. p-value: 0.577
  4. Decision: Since the p-value is greater than 0.05, we fail to reject the null hypothesis, suggesting there is no significant association between the number of followers and the sex of the players.

Would you like more details or have any questions? Here are some related questions to explore further:

  1. How would the results change if we used different follower category groupings?
  2. What are some alternative methods to assess the distribution of team followers?
  3. How can we account for potential confounding variables affecting the association between sex and the number of followers?
  4. What other variables in the dataset might influence the number of sponsors or win percentage?
  5. Could logistic regression provide additional insights into the factors influencing team success?

Tip: Always verify the assumptions of statistical tests, such as sample size and expected frequency requirements, before interpreting the results.

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Math Problem Analysis

Mathematical Concepts

Chi-square goodness-of-fit test
Chi-square test of independence
Hypothesis testing
Contingency tables

Formulas

Chi-square statistic: Χ² = Σ[(O - E)² / E]
Degrees of freedom (df) = (r-1)(c-1) for contingency tables
p-value calculation from Chi-square distribution

Theorems

Chi-square goodness-of-fit test
Chi-square test of independence

Suitable Grade Level

University level, Intermediate Statistics

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