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.
The cosine and cotangent values of angle Ф are
and -1. When the terminal side of an angle intersects the unit circle at point (x, y), then: The x-coordinate corresponds to the cosine of the angle formed with the positive x-axis and the terminal side, while the y-coordinate corresponds to the sine of that angle. Depending on the signs of x and y coordinates, we can determine the quadrant in which the angle resides.
If $24 is the price for the 5 used CDs, then your formula would be "24+5x" where x represents the count of additional CDs you buy.
24+5(6-5)
24+5(1)
24+5
=29
Thus, acquiring 6 CDs would cost $29
I hope that’s accurate, good luck^^
75,88,90,96,98,100
minimum = 75
Q1 = 88.....this indicates the start of the box
Q2 (the median) = (90 + 96) / 2 = 186/2 = 93....this signifies the line within the box
Q3 = 98....this indicates the end of the box
maximum = 100
88_93______98
75_______| | |___100
|___|_______|
Customers served in 0.5 hours : 3.6 versus x customers served in 7.5 hours
-------------------- = --------------------
0.5 hours 7.5 hours
Applying cross multiplication:
3.6 multiplied by 7.5 equals x times 0.5
Dividing both sides by 0.5:
x = (3.6 * 7.5) / 0.5
x = 54
So, you assisted 54 customers in 7.5 hours.
