Math Problem Statement

Research question: We wish to investigate whether employment status in the Sydney region is distributed according to the table below. employment status | Casual | Full-time | Part-time | Unemployed Percentage | 30 | 50 | 10 | 10 Please complete the following table calculating the values of A, B and C.

           | Casual | Full-time | Part-time | Unemployed | Total 

Observed Count | 34 | A=*** | 34 | 23 | 111
Expected Count | 33.3 | 55.5 | 11.1 | B=*** | 111
chi squared | C=*** | 22.707 | 47.244 | 12.758 | 82.724 A [integer]: Answer 1 Question 1 B [use at least 3dp]: Answer 2 Question 1

Solution

To find the missing values AA, BB, and CC, let’s analyze each part of the table:

Step-by-Step Calculations:

  1. Calculate AA: Observed Count for Full-time Since the total observed count is 111, we can find AA by subtracting the other observed counts: A=111(34+34+23)=11191=20A = 111 - (34 + 34 + 23) = 111 - 91 = 20 Therefore, A=20A = 20.

  2. Calculate BB: Expected Count for Unemployed The expected count for Unemployed can be calculated using the expected percentage of 10% of the total: B=0.10×111=11.1B = 0.10 \times 111 = 11.1 So, B=11.1B = 11.1 (to 3 decimal places as requested).

  3. Calculate CC: Chi-squared Value for Casual The chi-squared value for Casual is calculated using the formula: χ2=(OE)2E\chi^2 = \frac{(O - E)^2}{E} where OO is the observed count, and EE is the expected count. For Casual: C=(3433.3)233.3=0.7233.3=0.4933.30.0147C = \frac{(34 - 33.3)^2}{33.3} = \frac{0.7^2}{33.3} = \frac{0.49}{33.3} \approx 0.0147 Thus, C=0.0147C = 0.0147.

Final Answers:

  • A=20A = 20
  • B=11.1B = 11.1
  • C=0.0147C = 0.0147

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Math Problem Analysis

Mathematical Concepts

Statistics
Chi-Squared Test

Formulas

Chi-squared formula: χ² = (O - E)² / E

Theorems

Chi-squared distribution

Suitable Grade Level

Grades 11-12