A random sample of 5 states gave the following areas (in 1000 square miles; same data as Problem 2-38, incidentally): 147, 84, 24, 85, 159 a) Find the 95% confidence interval for the mean area for all 50 states in the United States. 13. A real estate agent wants to estimate the average selling price of houses in a suburb of Atlanta. It randomly samples 25 recent sales and calculates the average price = $148,000 and the standard deviation s = $62,000. a) Calculate a 95% confidence interval for the mean of all recent selling prices. 12. A random sample of 5 states gave the following areas (in 1000 square miles; same data as Problem 2-38, incidentally): 147, 84, 24, 85, 159 a) Find the 95% confidence interval for the mean area for all 50 states in the United States.

1. ) Computers in some vehicles calculate various quantities related to performance.  One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg).  For one vehicle equipped in this way, the car was set to 60 miles per hour by cruise control, and the mpg were recorded at random times.  Here are the mpg values from the experiment:

37.2     21.0     17.4     24.9     27.0     36.9     38.8     35.3     32.3     23.9

19.0     26.1     25.8     41.1     34.4     32.5     25.3     26.5     28.2     22.1

The vehicle sticker information for the vehicle states a highway average of 27 mpg.  Perform a hypothesis test at 5% significance level to determine if the results of this experiment are consistent with the vehicle sticker.

1. (30 points) Give the hypotheses, test statistic, rejection region, p-value, decision, and interpretation.
2. (5 points) What would a Type II error be in this situation?

Car A has a mass of 2000 kg and speed of 10 miles per hour. Car B has mass of 1000 kg and speed of 30 miles per hour. The two cars collide to each other and stick together after collision in three different situations. Calculate the velocity of the two cars after the collision.

1. Car A moves East and car B moves West and had a head to head collision. Calculate the velocity of the two cars after the collision (speed and direction).

2. Car B follows car A and both head toward the East. Car B had a head to tail collision with car A. Calculate the velocity for the two cars after the collision(speed and direction).

3.Car A moves to the East and car B moves to the North and collide in a cross road. Calculate the velocity for the two cars after the collision (speed and the angle of the velocity).

A certain statistics instructor participates in triathlons. The accompanying table lists times​ (in seconds) he recorded while riding a bicycle. He recorded every time he rode and randomly picked five laps through each mile of a​ 3-mile loop. Use a .05 significance level to test the claim that it takes the same time to ride each of the miles. Mile 1 194 205 203 202 201

Mile 2 198 201 200 196 200

Mile 3 215 211 209 212 209

a) State the null and alternative hypothesis (2 points).

b) Check the requirements (3 points)

c) Carry out the hypothesis test (make sure you write everything down) (3 points)

. d) What is your conclusion? (2 points)

e) Does one of the miles appear to have a​ hill? (2 points)

1. A study of a disease reveals that there is an average of 1 case every 22 square miles. Residents of a town that has an area of 10 square miles are concerned because there are two cases in their area. The state’s Department of Health has decided to investigate further if the probability of getting two or more cases in this town is less than 0.05. Does the Department of Health investigate further?   (3)

2. A lottery is carried out by choosing five balls, without replacement, from a box of 35 balls. The lottery ticket has five numbers on it. Find the probability that exactly four of the balls that come out of the box match the numbers on the lottery ticket. (3)

3. A neighborhood has 32 households – 27 white, and 5 nonwhite. A subset of 9 of these households move to an adjacent neighborhood. What is the probability that less than two of the households in the new neighborhood are nonwhite? (3)

AA purchased a van (cost: $50,000, salvage value: $5,000, useful life: 5 years).

1. Under straight-line method, how much is the book value at the end of 3^rd year of its useful life?

$18,000

$20,000

$23,000

$27,000

2. Under double-declining balance method, how much is the book value at the end of 5^thyear?

$2,333

$5,432

$6,221

None of the above

3. Under sum-of-years’ digits method, how much is the accumulated depreciation at the end of 3^rd year?

4. Under sum-of-years’ digits method, how much is the annual depreciation expense for 2^ndyear?

5. AA estimated the total usage of this van would be 100,000 miles. During the first year, this van was used for 30,000 miles. What is the amount of book value at the end of 1^st year?

enny, Inc., is looking at setting up a new manufacturing plant in South Park. The company bought some land six years ago for $8.1 million in anticipation of using it as a warehouse and distribution site, but the company has since decided to rent facilities elsewhere. The land would net $10.9 million if it were sold today. The company now wants to build its new manufacturing plant on this land; the plant will cost $22.1 million to build, and the site requires $960,000 worth of grading before it is suitable for construction.

What is the proper cash flow amount to use as the initial investment in fixed assets when evaluating this project? (Do not round intermediate calculations and enter your answer in dollars, not millions, rounded to the nearest whole number, e.g., 1,234,567.)

Rangers at the everglades national park, ride an air-boat, the mass of the air boat plus the rangers is 500 kg. The blades of the boat push on the air with 1000N, while moving the rangers experience an air resistance force of 200N directed opposite to the direction of motion, and the boat a water resistance of 250N. They move in straight line for 20s. Please complete the following tasks:

1. Draw the free-body diagram showing all forces acting on the air-boat ranger system.

2. Calculate the net force acting on the boat-ranger system;

3. Determine the accelerations of the air boat system;

4. What is the coefficient of friction between the water and the boat?

5. What is the velocity of the boat at the end of the 20s, if its initial velocity was 20 m/s?

6. How far did the boat travel in those 20s?

Parker & Stone, Inc., is looking at setting up a new manufacturing plant in South Park to produce garden tools. The company bought some land six years ago for $5.1 million in anticipation of using it as a warehouse and distribution site, but the company has since decided to rent these facilities from a competitor instead. If the land were sold today, the company would net $5.4 million. The company wants to build its new manufacturing plant on this land; the plant will cost $12.6 million to build, and the site requires $780,000 worth of grading before it is suitable for construction. What is the proper cash flow amount to use as the initial investment in fixed assets when evaluating this project? (Enter your answer as a positive value in dollars, not millions of dollars, e.g., 1,234,567.)

You may need to use the appropriate technology to answer this question.

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use α = 0.05.

Find the value of the test statistic for method of loading and unloading.

Find the p-value for method of loading and unloading. (Round your answer to three decimal places.)

p-value =

State your conclusion about method of loading and unloading.

Because the p-value ≤ α = 0.05, method of loading and unloading is not significant.Because the p-value > α = 0.05, method of loading and unloading is significant.    Because the p-value > α = 0.05, method of loading and unloading is not significant.Because the p-value ≤ α = 0.05, method of loading and unloading is significant.

Find the value of the test statistic for type of ride.

Find the p-value for type of ride. (Round your answer to three decimal places.)

p-value =

State your conclusion about type of ride.

Because the p-value > α = 0.05, type of ride is significant.Because the p-value > α = 0.05, type of ride is not significant.    Because the p-value ≤ α = 0.05, type of ride is significant.Because the p-value ≤ α = 0.05, type of ride is not significant.

Find the value of the test statistic for interaction between method of loading and unloading and type of ride.

Find the p-value for interaction between method of loading and unloading and type of ride. (Round your answer to three decimal places.)

p-value =

State your conclusion about interaction between method of loading and unloading and type of ride.

Because the p-value ≤ α = 0.05, interaction between method of loading and unloading and type of ride is significant.

Because the p-value ≤ α = 0.05, interaction between method of loading and unloading and type of ride is not significant.    

Because the p-value > α = 0.05, interaction between method of loading and unloading and type of ride is not significant.

Because the p-value > α = 0.05, interaction between method of loading and unloading and type of ride is significant.