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.
Response:
I am uncertain.
Step-by-step clarification:
Response:
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Detailed explanation of the process:
Answer: $434, 306.4
Step-by-step explanation:
From the information provided,
P= $163,000
R= 14% ; 14/100= 0.14
T=7 years
Using the formula,
A= Pr e^t
A= 163000*e^(0.14*7)
= 163000*e^(0.98)
= $434,306.4
