1.)
A mechanical. person is intrested in testing if tuning a car engine would improve the gas miliage. A simple random sample of 8 cars were selected to determine the milage (miles per gallon). Then each of the 8 cars were given a tune up

Data
After Tune up: 28.21, 29.4, 30.42, 29.67, 31.31, 29.68, 28.82, 29.38
Mean: 29.61
Standard Deviation: 0.94

Before Tune Up: 26.9, 26.37, 29.13, 28.46, 28.17, 27.67, 27.84, 27.18,
Mean: 27.72
Standard deviation: 0.89

Difference (After-Before): 1.31, 3.03, 1.29, 1.21, 3.14, 2.01, 0.98, 2.2,
Mean: 1.9
Standard Deviation: 0.84

1.) Are the 2 samples (Before and after Tune Mileage) independent or dependent? Explain

2.) Show which plot you would use to check your assumptions? Show picture of it

3.)Are their and serious violations of any other assumption plots? Explain

4.) What is your output? state below Explain why you chose this output

5.) What is your conclusion at a 5% confidence level?

In a two-page paper, identify the physics principles contained within the following scenario. Explain how these principals connect to Einstein's theory of relativity or in modern applications in physics. If you use a GPS option on your car or a mobile device, you are using Einstein's theory of relativity. Finally, provide another example from your own experience, then compare and contrast your scenario to the provided example below.

Scenario:

Mandy took a trip to Rome, Italy. She gazed out over the open ocean 20,000 feet below as her airplane began its descent to her final destination of Rome. It had been a long flight from New York to Rome, but she as she stretched, and her bones creaked as though she was old, she knew that in fact, she was a tiny bit younger than her compatriots back home, thanks to traveling at hundreds of miles per hour. In fact, time for her was running slowly compared to her friends in New York for two reasons: the speed at which she had traveled and the height of the airplane above the Earth. Neither, though, were noticeable.

To illustrate the effects of driving under the influence​ (DUI) of​ alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine​ teenagers, the time​ (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. Complete parts​ (a) and​ (b).

​Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

​(a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the​ experiment?

​(b) Use a​ 95% confidence interval to test if there is a difference in braking time with impaired vision and normal vision where the differences are computed as​ "impaired minus​ normal.

The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.

a. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.)

TaxesˆTaxes^  = ______ + ______ Size.

b. Interpret the slope coefficient.

• As Property Taxes increase by 1 dollar, the size of the house increases by 6.86 ft.

• As Size increases by 1 square foot, the property taxes are predicted to increase by $6.86.

c. Predict the property taxes for a 1,500-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

  TaxesˆTaxes^ ________

We are interested in exploring the relationship between the weight of a vehicle and its fuel efficiency (gasoline mileage). The data in the table show the weights, in pounds, and fuel efficiency, measured in miles per gallon, for a sample of 12 vehicles.

Find the correlation coefficient.

Find the equation of the best fit line. (Round your answers to four decimal places.)

What percent of the variation in fuel efficiency is explained by the variation in the weight of the vehicles, using the regression line? (Round your answer to the nearest whole number.

For the vehicle that weighs 3000 pounds, find the residual

(y − ŷ).

(Round your answer to two decimal places.)

Remove the outlier from the sample data. Find the new correlation coefficient and coefficient of determination. (Round your answers to two decimal places.)

Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the​ freeway, resulting in a freer flow of​ cars, which ultimately results in faster travel times. To test whether ramp metering is effective in reducing travel​ times, engineers conducted an experiment in which a section of freeway had ramp meters installed on the​ on-ramps. The response variable for the study was speed of the vehicles. A random sample of 15 cars on the highway for a Monday at 6 p.m. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 p.m. with the meters off resulted in the following speeds​ (in miles per​ hour).

Ramp_Meters_On   Ramp_Meters_Off
27   24
38   33
43   47
35   29
42   37
47   25
32   36
47   39
56   22
27   51
57   41
26   31
51   17
40   41
46   42

Determine the​ P-value for this test.

​P-value equals=.? ​(Round to three decimal places as​ needed.)

Tiffany is a model rocket enthusiast. She has been working on a pressurized rocket filled with nitrous oxide. According to her design, if the atmospheric pressure exerted on the rocket is less than 10 pounds/sq.in., the nitrous oxide chamber inside the rocket will explode. Tiff worked from a formula p=14.7e−h/10p=14.7e−h/10 pounds/sq.in. for the atmospheric pressure hh miles above sea level. Assume that the rocket is launched at an angle of αα above level ground at sea level with an initial speed of 1400 feet/sec. Also, assume the height (in feet) of the rocket at time tt seconds is given by the equation y(t)=−16t2+1400sin(α)ty(t)=−16t2+1400sin⁡(α)t. [UW]

a. At what altitude will the rocket explode?
b. If the angle of launch is αα = 12∘∘, determine the minimum atmospheric pressure exerted on the rocket during its flight. Will the rocket explode in midair?
c. If the angle of launch is αα = 82∘∘, determine the minimum atmospheric pressure exerted on the rocket during its flight. Will the rocket explode in midair?
d. Find the largest launch angle αα so that the rocket will not explode.

1.)In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 51 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 43 and 59?

2.)A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 38 months and a standard deviation of 3 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 41 and 47 months?

3.)he physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 60 and a standard deviation of 8. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 52 and 60?

The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.

a. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.)

taxes = ______ + ______ size

b. Interpret the slope coefficient.

a. As Property Taxes increase by 1 dollar, the size of the house increases by 6.78 ft.

b. As Size increases by 1 square foot, the property taxes are predicted to increase by $6.78.

c. Predict the property taxes for a 1,500-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

taxes _________