Based on sales over a six-month period, the five top-selling compact cars are Chevy Cruze, Ford Focus, Hyundai Elantra, Honda Ci

Question

6 days ago

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Based on sales over a six-month period, the five top-selling compact cars are Chevy Cruze, Ford Focus, Hyundai Elantra, Honda Ci

vic, and Toyota Corolla.† Based on total sales, the market shares for these five compact cars were Chevy Cruze 24%, Ford Focus 21%, Hyundai Elantra 20%, Honda Civic 18%, and Toyota Corolla 17%. Suppose a sample of 400 compact car sales in one city showed the following number of vehicles sold.
Chevy Cruze 108
Ford Focus 92
Hyundai Elantra 64
Honda Civic 84
Toyota Corolla 52
Use a goodness of fit test to determine if the sample data indicate that the market shares for the five compact cars in Chicago are different than the market shares reported by Motor Trend. Using a .05 level of significance

The p-value is

What is your conclusion?

What market share differences, if any, exist in Chicago?

Mathematics

1 answer:

tester [8.8K] · Answer 1 · 2026-03-22T11:06:01+03:00

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.