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jonny [76]
3 years ago
10

A dealer paid $10,000 for a boat at an auction. At the dealership, a salesperson sold the boat for 30% more than the auction pri

ce. The salesperson received a commission of 25% of the difference between the auction price and the dealership price. What was the salesperson’s commission?
Mathematics
1 answer:
pickupchik [31]3 years ago
7 0
<span>Given situation:
=> A deadler paid $10 000 for a boat at an auction.
=> At the dealership, a sales person sold the boat for 30% more than the auction price
=> 10 000 dollars + 30%
=> Then the salesperson received a commission of 25% of the difference between the auction price and the dealership price
=> 10 000 + 25%
Let’s find the solution
=> 10 000 x .30 = 3000
=> 10 000 + 3 000 = 13 000, he sell it for this price
=> then he received a commission
=> 13 000 – 3 000 = 10 000
=> 10 000 x .25
=> 2500 , his commission </span>



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1) χ² ≥ 11.07

2) Goodness of fit test, df: χ²_{3}

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The goodness of fit test has more degrees of freedom than the independence test.

3) e_{females.} = 80

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Step-by-step explanation:

Hello!

1)

The researcher took a sample of n=60 people and made them taste proof samples of six different brands of pizza and choose their favorite brand, their choose was recorded. So the study variable is the following:

X: favorite pizza brand, categorized in brand 1, brand 2, brand 3, brand 4, brand 5 and brand 6.

The Chi-square goodness of fit test is done with the following statistic:

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χ²_{k-1; 1 - \alpha }

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The statistic for the goodness of fit is:

χ²= ∑\frac{(O_i-E_i)^2}{E_i} ≈χ²_{k-1}

Degrees of freedom: χ²_{k-1}

In the example: k= 4 (the variable has 4 categories)

χ²_{4-1} = χ²_{3}

The statistic for the independence test is:

χ²= ∑∑\frac{(O_ij-E_ij)^2}{E_ij} ≈χ²_{(r-1)(c-1)} ∀ i= 1, 2, ..., r & j= 1, 2, ..., c

If the information is in a contingency table

r= represents the total of rows

c= represents the total of columns

In the example: c= 2 and r= 2

Degrees of freedom: χ²_{(r-1)(c-1)}

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The goodness of fit test has more degrees of freedom than the independence test.

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To calculate the expected frecuencies for the independence test you have to use the following formula.

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In the example: c= 3 and r= 4

Degrees of freedom: χ²_{(r-1)(c-1)}

χ²_{(3-1)(4-1)} = χ²_{6}

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