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:

  1. 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.

    A=113(22+28+34)=11384=29A = 113 - (22 + 28 + 34) = 113 - 84 = 29

    So, A = 29.

  2. 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:

    B=10100×113=0.1×113=11.3B = \frac{10}{100} \times 113 = 0.1 \times 113 = 11.3

    So, B = 11.3 (this value is already provided in the table).

  3. C (Chi-squared value for category "3 - 50,001 to 100,000 followers")

    The chi-squared statistic is calculated using the formula:

    χ2=(ObservedExpected)2Expected\chi^2 = \frac{(Observed - Expected)^2}{Expected}

    For category 3:

    C=(3456.5)256.5=(22.5)256.5=506.2556.58.961C = \frac{(34 - 56.5)^2}{56.5} = \frac{(-22.5)^2}{56.5} = \frac{506.25}{56.5} \approx 8.961

    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 Count22283429113
Expected Count11.311.356.533.9113
Chi-squared10.13224.6818.9610.70844.481

Would you like more details or have any other questions?


Here are five questions that build on this topic:

  1. How does the chi-squared statistic help determine the goodness of fit in this problem?
  2. What is the null hypothesis in this chi-squared test?
  3. How do we calculate degrees of freedom for a chi-squared test in this context?
  4. How does changing the observed counts affect the chi-squared value?
  5. 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.

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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