Question

In: Statistics and Probability

Graded problem #2. The table below gives the cost per unit of a manufactured piece as...

Graded problem #2. The table below gives the cost per unit of a manufactured piece as a function of the number of units produced. Take the number of units produced as the explanatory variable, x, and the cost per unit as the response variable y.

Units 10 20 50 100 150 200

Cost 140 155 153 150 180 160

a. Predict the cost per unit when 80 units are produced

b. Find a 90% confidence interval for the slope b1

c. Find a 90% confidence interval for the predicted value you found in answer b.

Solutions

Expert Solution

	X	Y	X * Y	X²	Ŷ	Sxx =Σ (Xi - X̅ )²	Syy = Σ( Yi - Y̅ )²	Sxy = Σ (Xi - X̅ ) * (Yi - Y̅)
	10	140	1400	100.0000	147.339	6136.106	266.777	1279.441
	20	155	3100	400.0000	148.488	4669.440	1.778	91.109
	50	153	7650	2500	151.932	1469.442	11.111	127.776
	100	150	15000	10000	157.673	136.112	40.111	-73.889
	150	180	27000	22500	163.414	3802.782	560.113	1459.447
	200	160	32000	40000	169.155	12469.452	13.445	409.448
Total	530	938	86150	75500	672.000	28683.333	893.333	3293.333

X̅ = Σ (Xi / n ) = 530/6 = 88.3333
Y̅ = Σ (Yi / n ) = 938/6 = 156.3333

Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X² - (ΣX)² )
b = ( 6 * 86150 - 530 * 938 ) / ( 6 * 75500 - ( 530 )²)
b = 0.1148

a =( ΣY - ( b * ΣX ) ) / n
a =( 938 - ( 0.1148 * 530 ) ) / 6
a = 146.1912
Equation of regression line becomes Ŷ = 146.1912 + 0.1148 X

Part a)

= 146.1912 + 0.1148 X
= 155.3752

Estimated Error Variance (σ̂²) =
S² = ( 893.3333 - 0.1148 * 3293.3333 ) / 6 - 2
S² = 128.814659
S = 11.3497

Part b)

Confidence Interval

= 2.132 ( Critical value from t table )

90% confidence interval is -0.0281 < < 0.2577

Part c)

Confidence Interval of
= 146.1912 + 0.1148 X
= 155.3752

= 2.132 ( From t table )
X̅ = (Xi / n ) = 530/6 = 88.3333
= 155.3752

90% confidence interval is ( 145.4252 < < 165.3252 )

orchestra answered 1 year ago

Next > < Previous

Related Solutions

For many years Miller Company manufactured television tubes in Massachusetts at a per unit cost of...

For many years Miller Company manufactured television tubes in Massachusetts at a per unit cost of $100 for direct labor, $50 for direct material, and $20 for overhead. A portion of production was sold to Fiona Manufacturing, Ltd., Miller´s wholly owned distribution affiliate in Ireland, for $220 per unit. The Irish affiliate incurred an additional $30 per unit of direct costs and resold to European television manufactures for $300 per unit. No other costs were involved, expect for income taxes...

For a table manufacturing company, selling price for a table is $203.00 per Unit, Variable cost...

For a table manufacturing company, selling price for a table is $203.00 per Unit, Variable cost is $23.00 per Unit, rent is $4,884.00 per month and insurance is $300.00 per month. Company wants to expand its business and improve the table quality, it wants to increase the selling price for a table to $305.00 per Unit, Variable cost to $59.00 per Unit, bigger area will have rent $6,985.00 per month and insurance is $421.00 per month At what point will...

For a table manufacturing company, selling price for a table is $161.00 per Unit, Variable cost...

For a table manufacturing company, selling price for a table is $161.00 per Unit, Variable cost is $25.00 per Unit, rent is $3,531.00 per month and insurance is $285.00 per month. Company wants to expand its business and improve the table quality, it wants to increase the selling price for a table to $290.00 per Unit, Variable cost to $57.00 per Unit, bigger area will have rent $5,704.00 per month and insurance is $389.00 per month At what point will...

The above table gives the quantity of output and the total cost for a perfectly competitive firm that can sell all of its output at $9 per unit

Quantity(units)Total cost(dollars)0316212321433549The above table gives the quantity of output and the total cost for a perfectly competitive firm that can sell all of its output at $9 per unita) Find the profit maximizing level of output for this firm.(Show your work and explain). (3 points) (world limit: 100)b) How much economic profit is the firm making?(Show your work and explain) (3 points) (world limit: 100)

2. The table below gives the list price and the number of bids received for five...

2. The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to...

The table below gives the opportunity cost that Ru Paul incurs for each evening during the...

The table below gives the opportunity cost that Ru Paul incurs for each evening during the week she performs. If she can perform as many evenings as she would like and receives €801.50 per evening she performs, how many evenings does Ru Paul perform each week? Q MC 1 €289 2 €341 3 €445 4 €531 5 €612 6 €720 7 €889

Data Manufactured in-house Fixed cost $50,000 Unit variable cost $125 Payoff Table Demand Purchased from supplier...

Data Manufactured in-house Fixed cost $50,000 Unit variable cost $125 Payoff Table Demand Purchased from supplier 800 1,000 1,200 1,400 Unit cost $175 Manufacture $150,000 $175,000 $200,000 $225,000 Outsource $140,000 $175,000 $210,000 $245,000 Production volume 1500 Model ANSWER Manufacture/Outsource Value Average Payoff Total manufacturing cost $237,500 Aggressive Total purchased cost $262,500 Conservative Cost difference (Manufacture - Purchase) -$25,000 Best Decision Manufacture Problem 16A Payoff Tables Based on the cost model and payoff table provided, determine the...

Per unit data concerning a product manufactured by XYZ Co. are given below: Selling price $100...

Per unit data concerning a product manufactured by XYZ Co. are given below: Selling price $100 Direct materials, direct labor, and variable manufacturing overhead 40 Fixed manufacturing overhead 25 Variable selling expense 10 Fixed selling and administrative expense 7 The above per unit data are based on annual production of 10,000 units. The company has received a special, one-time-only order for 500 units of the product with a selling price of $60. There would be no variable selling expense on...

An incomplete cost of goods manufactured schedule is presented below. Complete the cost of goods manufactured...

An incomplete cost of goods manufactured schedule is presented below. Complete the cost of goods manufactured schedule for Monty Company. MONTY COMPANY Cost of Goods Manufactured Schedule For the Month Ended December 31, 2017December 31, 2017For the Year Ended December 31, 2017 Work in process (1/1) $213,900 Direct materials Raw materials inventory (1/1) $ Add: Raw materials purchases 164,300 Total raw...

Use the information in the table below to answer the following questions. Production per unit of...

Use the information in the table below to answer the following questions. Production per unit of Labor U.S. Argentina Wheat 100 200 Beef 200 400 Does either country have an absolute advantage in the production of wheat or beef? Explain. (b) What is the opportunity cost of wheat in each country? (c) What is the opportunity cost of beef in each country? (d) Analyze comparative advantage and opportunities for trade between the U.S. and Argentina. Unit labor Requirements...

Subjects