Math Problem Statement
Research question: 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 (less that 10,000) | 2 (10,001-50,000) | 3 (50,001-100,000) | Percentage | 10 | 10 | 50 |
the number of followers of teams 4 (more that 100,001) Percentage 30 Please complete the following table calculating the values of A, B and C.
| 1 (less that 10,000) | 2 (10,001-50,000) | 3 (50,001-100,000) |
Observed Count | 22 | 28 | 34 |
Expected Count | B=*** | 11.3 | 56.5 |
chi squared | 10.132 | 24.681 | C=*** |
4 (more that 100,001) | Total
Observed Count A=*** | 113
Expected Count 33.9 | 113
chi squared 0.708 | 44.481
A [integer]: Answer 1 Question 2
29
B [use at least 3dp]:
Solution
To complete the table, we need to calculate the following values:
-
A (Observed Count for the category "4 - more than 100,001 followers")
To find this, we can use the total observed count (113) minus the sum of the observed counts for categories 1, 2, and 3.
So, A = 29.
-
B (Expected Count for the category "1 - less than 10,000 followers")
The expected count is calculated using the total expected count of 113 and the percentage for each category. The percentage for category 1 is 10%. Therefore, we can calculate:
So, B = 11.3 (this value is already provided in the table).
-
C (Chi-squared value for category "3 - 50,001 to 100,000 followers")
The chi-squared statistic is calculated using the formula:
For category 3:
So, C ≈ 8.961.
Updated Table
1 (less than 10,000) | 2 (10,001-50,000) | 3 (50,001-100,000) | 4 (more than 100,001) | Total | |
---|---|---|---|---|---|
Observed Count | 22 | 28 | 34 | 29 | 113 |
Expected Count | 11.3 | 11.3 | 56.5 | 33.9 | 113 |
Chi-squared | 10.132 | 24.681 | 8.961 | 0.708 | 44.481 |
Would you like more details or have any other questions?
Here are five questions that build on this topic:
- How does the chi-squared statistic help determine the goodness of fit in this problem?
- What is the null hypothesis in this chi-squared test?
- How do we calculate degrees of freedom for a chi-squared test in this context?
- How does changing the observed counts affect the chi-squared value?
- Why is it important to compare observed and expected counts in statistical analysis?
Tip: The chi-squared test is sensitive to sample size, so a larger sample can make small differences statistically significant.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Chi-squared Test
Expected and Observed Counts
Goodness of Fit
Formulas
Expected Count = (Percentage/100) x Total
Chi-squared = (Observed - Expected)^2 / Expected
Theorems
Chi-squared Goodness of Fit Test
Suitable Grade Level
Grades 11-12
Related Recommendation
Chi-Squared Test for Followers Distribution in Major International Team Sports
Chi-Squared Goodness-of-Fit Test for Team Follower Distribution
Chi-Square Test on Team Followers and Sex in Major International Competitions
Chi-square Test for Categorical Data: Learning Objectives and Formulas
Chi-Square Test for Egg Quality Control - Hypothesis Testing