A tire manufacturer claims that the life span of its tires is 52,000 miles. Assume the life spans of the tire are normally distributed. You selected 16 tires at random and tested them. The mean life span of the sample is 50,802 miles. The tires had a population standard deviation, σ = 800. Use the .05 level of significance. a) Which distribution would be indicated? b) Explain why you chose that distribution. c) Construct a confidence interval for the mean using the above data. Use the .05 level of significance. d) Re-compute the confidence interval if “n” is increased to 125 with the same mean and standard deviation. e) Re-compute the confidence interval if level of significance .01 with the same mean and standard deviation with the original n.

Ilya and Anya each can run at a speed of 8.30mph and walk at a speed of 3.90mph . They set off together on a route of length 5.00miles . Anya walks half of the distance and runs the other half, while Ilya walks half of the time and runs the other half.

How long does it take Anya to cover the distance of 5.00miles ?

Express your answer numerically, in minutes.

Find Anya's average speed.

Express Anya's average speed save,Anya numerically, in miles per hour.

How long does it take Ilya to cover the distance?

Express the time tIlya taken by Ilya numerically, in minutes.

Now find Ilya's average speed.

Express Ilya's average speed save,Ilya numerically, in miles per hour.

The accompanying table shows a portion of data consisting of the selling price, the age, and the mileage for 20 used sedans.

a. Determine the sample regression equation that enables us to predict the price of a sedan on the basis of its age and mileage. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) [If you are using R to obtain the output, then first enter the following command at the prompt: options(scipen=10). This will ensure that the output is not in scientific notation.]

b. Interpret the slope coefficient of Age.

• The slope coefficient of Age is −528.13, which suggests that for every additional year of age, the predicted price of car decreases by $528.13.

• The slope coefficient of Age is −0.09, which suggests that for every additional year of age, the predicted price of car decreases by $0.09.

• The slope coefficient of Age is −528.13, which suggests that for every additional year of age, the predicted price of car decreases by $528.13, holding number of miles constant.

• The slope coefficient of Age is −0.09, which suggests that for every additional year of age, the predicted price of car decreases by $0.09, holding number of miles constant.

c. Predict the selling price of a seven-year-old sedan with 66,000 miles. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

Which hypothesis test you believe you should use and why.

• One Sample Proportion Z-test

• Two Sample Proportion Z-test

• One Mean t-test

• Pooled t-test

• Non-Pooled t-test

• Paired t-test

• ANOVA F-test

• Bootstrapping is also an option

Questions:

4. The NOAA National Climatic Data Center of the United States provides data on the average annual temperature for every state in the United States. The average annual temperatures are based on data collected by weather stations throughout each state during the years 1971 to 2000. Is there strong evidence that the mean average annual temperature in the United States is greater than 50 degrees Fahrenheit? Explain. Use a significance level of 5%.

5. As gas prices continue to rise, more customers are beginning to take into account miles per gallon (a measure of the average distance traveled per unit of energy consumed) when determining which type of car to purchase. Do cars made in Japan typically get more miles per gallon than cars made in the United States? A random sample of 79 cars made in Japan had a mean of 30.48 and a standard deviation of 6.11 miles per gallon. A random sample of 249 cars made in the United States produced a mean of 20.14 and a standard deviation of 6.41 miles per gallon. Use a significance level of 0.10.

6. The U.S. Census Bureau reports that 26% of all U.S. businesses are owned by women. A Colorado consulting firm surveys a random sample of 410 businesses in the Denver area and finds that 115 of them have women owners. Should the firm conclude that its area is unusual? Test an appropriate hypothesis and state your conclusion. Use =0.05.

Problem 2: Maximizing Net Benefits

There are important trade-offs involved in granting "Wild and Scenic River Status" to portions of a river. How much of this public good, a free-flowing river, should be protected from further development? As an analyst in the Office of Policy Analysis of the U.S. Department of the Interior, you are called upon to make a recommendation. Each year, 1,000 people benefit from the river's various services. A contingent valuation survey carried out by your office has estimated that each individual beneficiary has the same demand function for river preservation,

Q = 75 - (0.25)(P)

where P is the price-per-mile which persons are willing to pay (per year) for Q miles of river preserved. You find that the marginal (opportunity) cost of preservation is $60,000 per mile per year. ($60,000 for every one mile)

[Hint: You need to derive the market (aggregate) demand curve for a public good.]

a)How many miles of the river would be preserved in an efficient allocation?

b) What is the magnitude of the total (gross), annual benefits associated with this (efficient allocation) policy?

c)What are the total, annual costs of the policy?

d) What is the magnitude of the total (annual) consumers' surplus?

e)How large are net, annual benefits?

f) If it turns out that the marginal cost of preservation is only $20,000 per mile per year, how many miles of the river would be preserved in an efficient allocation?

g) Now assume substitute sites are available to beneficiaries, so their demands are substantially more elastic: their individual demand functions for river preservation are Q = 75 - (0.75)(P) In this case, with the original marginal costs of preservation of $60,000 per mile per year, how many miles of the river would be preserved in an efficient allocation?

A consumer agency claims that the average fuel mileage of Sedan A exceeds that of Sedan B. To test this claim, a random sample of 17 Sedan A vehicles were tested and the sample mean fuel mileage was found to be 28.25 miles per gallon with a known population standard deviation of 1.30 miles per gallon. A random sample of 14 Sedan B vehicles also were tested and the sample mean fuel mileage was found to be 27.25 miles per gallon with a known population standard deviation of 1.35 miles per gallon. Use a 1% significance level and assume the fuel mileage values for each of the two populations of sedans are normally distributed.

a. Select the correct symbol to replace "?" in the null hypothesis H₀: μ_A − μ_B? 0

b. Select the correct symbol to replace "?" in the alternative hypothesis H_a: μ_A − μ_B? 0

c. Compute the value of the test statistic used to test the agency's claim.

Do not round any intermediate calculations. Round your answer to two decimal places. Enter a "−" sign directly before a negative answer.

Test statistic =

d. Determine the critical value used to test the agency's claim.

Enter your critical value to three decimal places. Enter a "−" sign directly before a negative answer.

Critical value =

e.  Compute the p-value for this hypothesis test.

Use your rounded test statistic from Part c. Do not round any other intermediate calculations. Round your final answer to four decimal places.

p-value =

f. Based on the above results, choose the appropriate initial conclusion.

g. Based on the claim and your initial conclusion, choose the appropriate final conclusion.

Account Analysis Method Shirrell Blackthorn is the accountant for several pizza restaurants based in a tri-city area. The president of the chain wanted some help with budgeting and cost control, so Shirrell decided to analyze the accounts for the past year. She divided the accounts into four different categories, depending on whether they appeared to be primarily fixed or to vary with one of three different drivers. Food and wage costs appeared to vary with the total sales dollars. Delivery costs varied with the number of miles driven (workers were required to use their own cars and were reimbursed for miles driven). A group of other costs, including purchasing, materials handling, and purchases of kitchen equipment, dishes, and pans, appeared to vary with the number of different product types (e.g., pizza, salad, and lasagna). Shirrell came up with the following monthly averages: Food and wage costs $ 155,000 Delivery costs $ 22,950 Other costs $ 260 Fixed costs $ 265,000 Sales revenue $ 650,000 Delivery mileage in miles 9,000 Number of product types 20 Required: 1. Calculate the average variable rate for the following costs: food and wages, delivery costs, and other costs. If required, round your answers to two decimal places. Use your rounded answers in subsequent computations if necessary. Average Variable Rate Food and wages % Delivery costs $ per mile Other costs $ per product 2. Form an equation for total cost based on the fixed costs and your results from Requirement 1. Enter the sales percent in decimal form, rounded to four decimal places. For example, 62.75% would be entered as 0.6275. Total cost = $ + (sales) + $ (miles) + $ (product) 3. The president is considering expanding the restaurant menu and plans to add one new offering to the menu. According to the cost equation, what is the additional monthly cost for the new menu offering? $

The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends on many factors, including the model year, mileage, and condition. To investigate the relationship between the car’s mileage and the sales price for Camrys, the following data show the mileage and sale price for 19 sales (PriceHub web site, February 24, 2012).

5- The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $10 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.3 million with a 0.2 probability, $2.4 million with a 0.5 probability, and $0.7 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations. Debt/Capital ratio is 0

RÔE = %

σ = %

CV =

Debt/Capital ratio is 10%, interest rate is 9%.

RÔE = %

σ = %

CV =

Debt/Capital ratio is 50%, interest rate is 11%.

RÔE = %

σ = %

CV =

Debt/Capital ratio is 60%, interest rate is 14%

RÔE = %

σ = %

CV =