determined that the variable cost
SuperClassBUS 305 Name ____________________________
41 points possible
you may use your book, notes, StatCrunch and Excel, but you must not collaborate with any other person in any way.
1. Functions (8 points)
a. The Santara Leather Company makes fine leather objects. The company has determined that the variable cost to make one kind of its purses is $84 and the fixed cost of production is $2200. Write the total cost function, letting x be the number of purses that are made and sold.
C(x) =
b. Santara has a contract to sell these purses to a store for $125 each. Write the revenue function, letting x be the number of purses that are made and sold.
R(x) =
c. Write the function for profit, letting x be the number of purses that are made and sold. Simplify.
P(x) =
d. What is the profit when 100 purses are made and sold?
2. Understanding the derivative (5 points)
The derivative of a function is
a. When x = 50, is the function increasing or decreasing? Explain.
b. Where is the function changing more steeply—at x = 10 or at x = 20? Explain.
3 Understanding the derivative (7 points)
The Santara Leather Company knows that price and demand for its laptop case are related according to this formula: , where p is the price they will charge.
a. How much revenue will they make? Using p as the price and the demand function above, write revenue as a function of p and simplify. Remember: price times demand = revenue.
b. What is the marginal revenue when the price is $250?
c. Is it a good idea for the company to think about increasing the price of the laptop bag above $250? Explain.
Problems 4 – 6 are worth 3 points each. Highlight the best answer for each.
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7. (3 points) Which is the best description of the time series data shown in this plot?
a. monthly data, positive trend, no seasonality, 8 cycles
b. quarterly data, positive trend, seasonality
c. annual data, no trend, multiple cycles
d. daily data for one month, no trend, daily seasons
8. (5 points) Records from a real estate office provide information about a sample of 800 properties. Use this data to test the hypothesis that the listing price and the number of days until sold are independent. Portions of StatCrunch output for this test follow.
Days until sold | ||||
Initial price | Under 30 | 31 to 90 | Over 90 | Total |
Under $150,000 | 50 | 40 | 10 | 100 |
$150,000 to $199,000 | 20 | 150 | 80 | 250 |
$200,000 to $250,000 | 20 | 280 | 100 | 400 |
Over $250,000 | 10 | 30 | 10 | 50 |
Total | 100 | 500 | 200 | 800 |
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Under 30 | 31 to 90 | Over 90 | Total | |
Under $150,000 | 50 | 40 | 10 | 100 |
$150,000 to $199,000 | 20 | 150 | 80 | 250 |
$200,000 to $250,000 | 20 | 280 | 100 | 400 |
Over $250,000 | 10 | 30 | 10 | 50 |
Total | 100 | 500 | 200 | 800 |
Chi-Square test:
Statistic | DF | Value | P-value |
Chi-square | 6 | 163.2 |
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a. The expected number of properties in the Under $150,000 row and Under 30 column has been x’d out. What value should appear there? Explain how this number would be calculated.
b. With .05 in the tail and 6 degrees of freedom, the critical chi square value is 12.592. As the output indicates, the value of the sample test statistic is 163.2. Is the p-value for this test larger or smaller than .05? Explain your answer.
c. Is price independent of listing time? Explain.
9. (4 points)For the last few years, patron contributions to the Arts Fund have been distributed according to the following proportions:
Description | Portrait (up to $100) | Landscape (up to $500) | Renaissance (up to $1000) | Old Master (over $1000) |
Proportion | .35 | .30 | .20 | .15 |
Lately, however, the fund directors are concerned that the economy may have impacted giving.
a. State the appropriate null and alternative hypotheses to address this concern.
b. Describe what statistical test should be used to test this hypothesis.
10 years ago
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