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

To find the missing values \( A \), \( B \), and \( C \), let’s analyze each part of the table:

### Step-by-Step Calculations:

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

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

3. **Calculate \( C \): Chi-squared Value for Casual**
   The chi-squared value for Casual is calculated using the formula:
   \[
   \chi^2 = \frac{(O - E)^2}{E}
   \]
   where \( O \) is the observed count, and \( E \) is the expected count. For Casual:
   \[
   C = \frac{(34 - 33.3)^2}{33.3} = \frac{0.7^2}{33.3} = \frac{0.49}{33.3} \approx 0.0147
   \]
   Thus, **\( C = 0.0147 \)**.

### Final Answers:
- **\( A = 20 \)**
- **\( B = 11.1 \)**
- **\( C = 0.0147 \)**

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

Investigate if employment status in Sydney follows expected distribution percentages for Casual, Full-time, Part-time, and Unemployed roles. Learn to calculate observed, expected counts, and chi-squared values for key categories, using formulas for statistical analysis. Suitable for Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation