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.
I believe the correct responses are AB and AE, but I would need an image to confirm.
<span>The flag's dimensions are 40 inches by 55 inches.
Reasoning<span>:
The perimeter equals the sum of all sides. Being rectangular, opposite sides have equal lengths. Thus, the equation is
y + 11/8 y + y + 11/8 y = 190.
Simplifying, we get
2y + 22/8 y = 190.
Expressing 22/8 as a mixed fraction results in
2y + 2 3/4 y = 190.
Combining terms: 4 3/4 y = 190.
Divide both sides by 4 3/4:
y = 190 ÷ 4 3/4.
Converting 4 3/4 to an improper fraction: y = 190 ÷ 19/4.
Dividing by a fraction means multiplying by its reciprocal:
y = 190 × 4/19 = 760/19 = 40.
Since y = 40, calculate 11/8 y = 11/8 × 40 = 440/8 = 55.</span></span>
