SOLUTION: Given the following calculate the test statistic, If convenient, use technology: a=0.10 Type of worker Professional Personal Both Technical 38

Question 1179289: Given the following calculate the test statistic, If convenient, use technology:
a=0.10
Type of worker Professional Personal Both
Technical 38 35 34
Other 49 30 34
Answer by CPhill(2189) (Show Source): You can put this solution on YOUR website!
To calculate the test statistic for this contingency table, we will use the chi-square test for independence.
1. Set up the Hypothesis:
Null Hypothesis (H0): The type of worker and the category (Professional, Personal, Both) are independent.
Alternative Hypothesis (H1): The type of worker and the category are dependent.
2. Create the Contingency Table:
Type of Worker Professional Personal Both Total
Technical 38 35 34 107
Other 49 30 34 113
Total 87 65 68 220
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3. Calculate the Expected Frequencies:
The expected frequency for each cell is calculated as:
Expected Frequency = (Row Total * Column Total) / Grand Total
Expected (Technical, Professional) = (107 * 87) / 220 ≈ 42.34
Expected (Technical, Personal) = (107 * 65) / 220 ≈ 31.65
Expected (Technical, Both) = (107 * 68) / 220 ≈ 33.01
Expected (Other, Professional) = (113 * 87) / 220 ≈ 44.66
Expected (Other, Personal) = (113 * 65) / 220 ≈ 33.35
Expected (Other, Both) = (113 * 68) / 220 ≈ 34.99
4. Calculate the Chi-Square Statistic:
The chi-square statistic (χ²) is calculated using the formula:
χ² = Σ [(Observed - Expected)² / Expected]
χ² = [(38 - 42.34)² / 42.34] + [(35 - 31.65)² / 31.65] + [(34 - 33.01)² / 33.01] + [(49 - 44.66)² / 44.66] + [(30 - 33.35)² / 33.35] + [(34 - 34.99)² / 34.99]
χ² ≈ 0.457 + 0.354 + 0.029 + 0.413 + 0.334 + 0.028
χ² ≈ 1.615
Using Technology:
As shown by the provided python code, using the scipy library the chi-square statistic is calculated as 1.612983358368212.
Answer:
The test statistic (chi-square statistic) is approximately 1.613.
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