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 , , and , let’s analyze each part of the table:
Step-by-Step Calculations:
-
Calculate : Observed Count for Full-time Since the total observed count is 111, we can find by subtracting the other observed counts: Therefore, .
-
Calculate : Expected Count for Unemployed The expected count for Unemployed can be calculated using the expected percentage of 10% of the total: So, (to 3 decimal places as requested).
-
Calculate : Chi-squared Value for Casual The chi-squared value for Casual is calculated using the formula: where is the observed count, and is the expected count. For Casual: Thus, .
Final Answers:
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Chi-Square Test for Employment Status Distribution in Sydney
Chi-Square Goodness-of-Fit Test for Employment Status Distribution in Sydney
Chi-Square Test for Independence on Sex and Employment Status
Chi-Squared Test for Age Distribution in University Statistics Students
Chi-square Goodness-of-Fit Test for Age Distribution in Statistics at Macquarie University