Hi! The goal of the Chi-Square Goodness of Fit test is to determine if observed frequencies of a categorical variable align with the expected historical or theoretical values in the population. Having the sales proportions of the top-five compact cars, we compare them against 400 compact car sales data from Chicago to see if there are discrepancies. Specifically, we have:
- Chevy Cruze 24% ⟹ P(CC) = 0.24
- Ford Focus 21% ⟹ P(FF) = 0.21
- Hyundai Elantra 20% ⟹ P(HE) = 0.20
- Honda Civic 18% ⟹ P(HC) = 0.18
- Toyota Corolla 17% ⟹ P(TC) = 0.17
The hypotheses established are:
H₀: P(CC) = 0.24; P(FF) = 0.21; P(HE) = 0.20; P(HC) = 0.18; P(TC) = 0.17
H₁: There is a discrepancy between expected and observed outcomes.
With α set at 0.05, the statistic calculated is based on Oi (observed frequency) and Ei (expected frequency). The initial step involves calculating expected frequencies using: Ei = n * Pi, where Pi is the theoretical proportion for each category stated in the null hypothesis. The test conducted is right-tailed, and so is the p-value, calculated as: P(X²₄ ≥ 11.23) = 1 - P(X²₄ < 11.23) = 1 - 0.98 = 0.02. Since the p-value is lower than α, we reject the null hypothesis, indicating that Chicago's market shares for the five compact cars differ from those reported by Motor Trend.
Max's initial distance from Kim
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