The data below is the mileage (thousands of miles) and age of your cars .

Year Miles Age

2017    8.5    1

2009 100.3    9

2014   32.7    4

2004 125.0   14

2003 115.0   15

2011   85.5    7

2012   23.1    6

2012   45.0    6

2004 123.0   14

2013   51.2    5

2013 116.0    5

2009 110.0    9

2003 143.0   15

2017   12.0    1

2005 180.0   13

2008 270.0   10

Please include appropriate Minitab Results when important

a. Identify terms in the simple linear regression population model in this context.

b. Obtain a scatter diagram for the sample data. Interpret the scatter diagram.

c. Obtain a scatter diagram with the least squares regression line included. Interpret the intercept and slope in the context of this problem.

d. In theory what ought to be the value of the population model intercept? Explain.

e. What is the informal prediction for what the mileage should be on your car? What is the error in the prediction of the mileage for your car?

f .Use some statistical reasoning to assess whether or not the prediction for the mileage on your car was “accurate”?

g. How would you respond if someone asks “about” how many miles do students drive per year?

The accompanying data represent the miles per gallon of a random sample of cars with a​ three-cylinder, 1.0 liter engine.

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(a) Compute the​ z-score corresponding to the individual who obtained

36.336.3

miles per gallon. Interpret this result.The​ z-score corresponding to the individual is

nothing

and indicates that the data value is

nothing

standard​ deviation(s)

▼

the

▼

​(Type integers or decimals rounded to two decimal places as​ needed.)

​(b) Determine the quartiles.

Q1equals=nothing

mpg

​(Type an integer or a decimal. Do not​ round.)

Q2equals=nothing

mpg

​(Type an integer or a decimal. Do not​ round.)

Q3equals=nothing

mpg

​(Type an integer or a decimal. Do not​ round.)

​(c) Compute and interpret the interquartile​ range, IQR. Select the correct choice below and fill in the answer box to complete your choice.

​(Type an integer or a decimal. Do not​ round.)

A.

The interquartile range is

nothing

mpg. It is the range of the observations between either the lower or upper quartile and the middle​ quartile; it captures​ 25% of the observations.

B.

The interquartile range is

nothing

mpg. It is the range of the observations between the lower and upper fences.

C.

The interquartile range is

nothing

mpg. It is the range of the middle​ 50% of the observations in the data set.

D.

The interquartile range is

nothing

mpg. It is the range of all of the observations in the data set.

​(d) Determine the lower and upper fences. Are there any​ outliers?

The lower fence is

nothing.

​(Type an integer or a decimal. Do not​ round.)

The upper fence is

nothing.

​(Type an integer or a decimal. Do not​ round.)

Are there any​ outliers? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The​ outlier(s) is/are

nothing.

​(Type an integer or a decimal. Do not round. Use a comma to separate answers as​ needed.)

B.

There are no outliers.

In a hypothetical island that is 5,000 miles away from humanity and includes no frictions in the market other than human nature, there are many shipping companies going back and forth that carry goods produced in the island to the world outside the island. There is also a dock to load these goods to the ships. The shipping industry is perfectly competitive.

In the island, there is a cement factory. The price per unit of cement at the door of the factory is $200 and the world price of same cement per unit is $350. But cement should be carried to the dock to be loaded in the ships. There are two means for transporting cement to the dock: i) a pipeline that pumps the cement to the dock (Company P) and ii) truck companies. There are many truck companies in the island and this industry is also perfectly competitive. Both the pipeline and the truck companies have identical services both in terms of price, speed, and amount carried each time. Truck companies can carry any item produced in the island, but the pipeline can only carry cement.

10 years ago, Company C and Company P signed a contract that set the price per unit of cement carried through the pipeline as $25 (10 years from that date, which is today, the price per unit of cement carried is also $25 for truck companies). This contact will expire tomorrow at 8 am and the companies met to negotiate the new terms of the contract.

1. What should be the new price for this new contract, if the two companies can agree on it? Why? Explain your rationale behind this prediction.

2. What can Company P do to maximize its benefits or survive? (Hint: since this is a hypothetical world, the capital markets are efficient)

Will rate for correct answers! :)

It is advertised that the average braking distance for a small car traveling at 75 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 38 small cars at 75 miles per hour and records the braking distance. The sample average braking distance is computed as 112 feet. Assume that the population standard deviation is 20 feet. (You may find it useful to reference the appropriate table: z table or t table)

a. State the null and the alternative hypotheses for the test.
  

• H₀: μ = 120; H_A: μ ≠ 120

• H₀: μ ≥ 120; H_A: μ < 120

• H₀: μ ≤ 120; H_A: μ > 120

b. Calculate the value of the test statistic and the p-value. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  

Find the p-value.
  

• 0.025 p-value < 0.05
• 0.05 p-value < 0.10
• p-value 0.10

• p-value < 0.01

• 0.01 p-value < 0.025

c. Use α = 0.10 to determine if the average breaking distance differs from 120 feet.
  

It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 34 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 116 feet. Assume that the population standard deviation is 22 feet. (You may find it useful to reference the appropriate table: z table or t table) b. Calculate the value of the test statistic and the p-value. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For the data from the first 11​ cars, the​ least-squares regression line is y=−0.0062x+42.4755. A twelfth car weighs 2,705 pounds and gets 14 miles per gallon. Compute the coefficient of determination of the expanded data set​ (including the twelfth​ car). What effect does the addition of the twelfth car to the data set have on Rsquared2​?

Car   Weight_(pounds)_x   Miles_per_Gallon_y
1   3765   21
2   3980   19
3   3532   22
4   3174   21
5   2582   27
6   3729   18
7   2601   26
8   3775   18
9   3313   19
10   2991   26
11   2753   26
12   2705   14

1) The coefficient of determination of the expanded data set is

2)How does the addition of the twelfth car to the data set affect Rsquared2​? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

a) It increases by __

b) It decreases by __

c) it does not affect it

It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 37 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 111 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the appropriate table: z table or t table) a. State the null and the alternative hypotheses for the test. H0: μ = 120; HA: μ ≠ 120 H0: μ ≥ 120; HA: μ < 120 H0: μ ≤ 120; HA: μ > 120 b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) b-2. Find the p-value. 0.01 p-value < 0.025 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10 p-value < 0.01 c. Use α = 0.01 to determine if the average breaking distance differs from 120 feet.

To get to a concert in time, a harpsichordist has to drive 122 miles in 1.93 hours. (a) If he drove at an average speed of 52.0 mi/h in a due west direction for the first 1.22 h, what must be his average speed if he is heading 30.0° south of west for the remaining 42.6 min?(b) What is his average velocity for the entire trip?(give magnitude and direction)