The developer of a new filter for filter-tipped cigarettes claims that it leaves less nicotine in the smoke than does the current filter. Because cigarette brands differ in a number of ways, he tests each filter on one cigarette of each of nine randomly selected brands and records the difference in nicotine content. His results are given in the table below.

Does the data give convincing evidence that the filter tips leave less nicotine in the smoke? Follow the 4-step process.

old=c(.7, .8, .8, .9, .9, 1, 1.2, 1.2, 1.8)

new=c(.6, .6, .7, .8, .7, 1, .8, .9, 1.5)

YOU MUST FOLLOW THE 4-STEP PROCESS

STATE:

PLAN:

DO:

CONCLUSION:

Thank you!

N12R.3Imagine you are the orbital engineer for the first NASA space shot to Ceres, the largest known asteroid. Ceres’s nearly circular orbit around the sun has a radius of R = 2.77 AU. After being launched from the earth, the probe will initially be in a circular orbit around the sun with the same radius (rc = 1.0 AU) and the same orbital speed Inline_Formula as the earth’s orbit. The probe’s rocket engines will then fire briefly to increase the probe’s speed to that speed Inline_Formula needed to put the probe into an elliptical orbit whose initial (and minimum) distance from the sun is rc = 1.0 AU and whose final (and largest) distance from the sun is R = 2.77 AU (this is a Hohmann transfer orbit). (a) How long will it take the probe to get from the earth to Ceres in such an orbit? (b) What is the speed Inline_Formulathat the probe has to have just after firing its engines to be inserted into this orbit? (Assume the duration of the boost is short enough that its distance from the sun is still nearly rc just after the engines have been fired.)

You are working in the cancer therapy division of a hospital. This hospital treats cancer by hitting a tumor with high energy protons from a cyclotron. When the protons leave the cyclotron they are going at half the speed of light. You are in charge of deflecting the protons so they hit the patent's tumor. This deflection is accomplished by passing the proton beam between two flat, parallel electrodes that have a length of 10.0 feet in the entering beam direction. The protons enter the region between the electrodes going parallel to their surface. The two electrodes are separated by 1.5 inches. A high voltage is applied to the electrodes so that the protons passing between them have a constant acceleration as they are attracted directly toward one plate and repelled by the other. After the protons leave the region between the plates, they are no longer accelerated during the remaining 200 feet to the patient. To set the correct high voltage, you need to calculate the magnitude of the acceleration the protons need when they are between the plates so that they are deflected by 1.0 degree, the angle between the incident beam and the beam hitting the patient. The speed of light is 1.0 foot per nanosecond.

Trace the following program. This means you need to fill the table in which you show the output of each executed instruction as if you are the computer executing the program. Put your comments under the table.

#include<iostream>

using namespace std;

int main ()

{

cout.setf(ios :: fixed);

cout.setf(ios :: showpoint);

cout.precision(2);

int A=7.5, B=2.5, C;                                                                                        //statement 1

double X,Y;

char Letter;

C = A/B;                                                                                                          //statement 2

X = 1.0*A/B;                                                                                                    //statement 3

if (C<X)

        Letter = 30*C;                                                                                         //statement 4

if (C=X)

        Letter = 20*C;                                                                                         //statement 5

if (C>X)

        Letter = 10*C;                                                                                         //statement 6

cout << "Letter = " << Letter+10 << endl;                                                       //statement 7

Letter = Letter + 10;                                                                                        //statement 8

cout << "Letter = " << Letter << endl;                                                             //statement 9

Y = 1.0*(A/B);                                                                                                 //statement 10

X = Y/ (B+5) + 2.5;                                                                                          //statement 11

cout.precision(1);

cout << "X = " << X << endl;                                                                           //statement 12

return 0;

}

Use the following information for the next 7 problems:

A simple random sample of 40 recorded speeds is obtained from cars traveling on a section of interstate 405 in Los Angeles. The sample has a mean of 68.4 miles per hour and a standard deviation of 5.7 miles per hour.

We wish to test the hypothesis that the mean speed of cars on this stretch of road is higher than the posted speed limit of 65 miles per hour. Test at a 0.5 level.

Question 15: What do yoy need to write down for the DATA SUMMARY of this problem?

A. sample size, number of successes, sample proportion

B. Sample size, sample mean, standard deviation

C. sample size, sample mean, population standard deviation

Question 16: Which of the following decribes the null and alternation hypothesis for this problem:

A. H0 u = 65, H1 u > 65

B. H0 u =68.4, H1 u <68.4

C. H0 u = 65, H1 u =/ 65

D. H0 u =68.4, H1 u =/ 68.4

Question 17: Which command in stat crunch do you use here?

A. z stats

B. T stats

C. Proportion stats

D. variance stat

Question 18: What is the p-value for this problem?

A. 0.05

B. 0.006

C. 0.003

D. 0.997

Question 19: do we reject the null hypothesis at the 0.05 level here?

A. Yes

B. No

Question 20: In plain english, what is the conclusion to the hypothesis test here?

A. the population mean speed is 68.4 MPH

B. The population mean speed is less than 68.4 MPH

C. The population mean speed is not 65 MPH

D. The population mean speed is faster that 65 MPH

Question 21: Calculate the 90% confidence interval estimate for the mean speed on I 405 in Los Angleles. We are 90% confident that the mean speed on I 405 is between 66.9 MPH and __________?

A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected.
(a) Develop a scatterplot with Distance to Work (miles) as the independent variable. Format the scatterplot to your preferences with the proper labels on the axes. In a textbox describe the relationship, if any, between the two variables. Add a linear trendline to the scatterplot, displaying the equation and R-squared value on the chart. [The scatterplot may be placed on this worksheet, a new worksheet or it's own sheet, as long as the chart is a respectable size for grading purposes.]
(b) On a new worksheet, labeled Calculations, create a table to calculate the estimated regression equation as the example in the text (Table 4.2) and the example done in class. Terms to calculate will be X-bar; Y-bar; (X - X-bar); (Y - Y-bar); (X - X-bar)*(Y - Y-bar); (X - X-bar)2. Calculate the slope coefficient (b1) and intercept (b0) in Excel using the table. Write the estimated regression equation.
(c) On a new worksheet, labeled Regression, provide the regression analysis using the Data Analysis addin tool. (You may wish to answer the following questions in a textbox.)
i. Write the estimated regression equation from the regression output.
ii. Interpret the coefficient for the independent variable, i.e. if X were to change, what is the result to Y.
iii. Interpret the coefficient of determination (R2) for the model.
iv. Test for the significance of the relationship at the 0.05 level of significance.
(d) Using the estimated regression equation, calculate the expected number of days absent for employees living 5 miles from the company


Distance to Work Number of Days Absent
1 8
3 5
4 8
6 7
8 6
10 3
12 5
14 2
14 4
18 2

Read the following scenario and complete each of the seven problems below:

A new car manufacturing company has emerged and has claimed that its new hybrid car, the Pusho, gets a better gas mileage than the highest ranked Toyota Prius. Consumer Reports Magazine decides to test this claim at a 5% level of significance. Consumer Reports randomly selects 10 of each type of car, calculates the miles per gallon for each car in the study, and records the data in the table below. Assume miles per gallon of the cars is normally distributed.

Pusho 54.1     52.4    55.7 49.7   50.6      48.9    51.8    54.5    56.9    49.8

Prius   53.2     54.3    49.8    50.1    50.5     56.1    47.8    53.4    56.8    48.7

A. Evaluate the claim that the Pusho gets a better gas mileage than the highest ranked Prius using the data from the Consumer Reports study.

1. Identify the type of test you will use to test this claim. Explain your reasoning. 2. State the null and alternate hypotheses. 3. Conduct the hypothesis test and determine the p-value. 4. State your conclusion about the claim. 5. Construct a 90% confidence interval for this study.

1.

2.

3.

4.

5.

Suppose that Toyota makes a counter-claim that their Prius has a higher gas mileage than Pusho. How could the alternative hypotheses from Part A be changed to test Toyota’s claim? Conduct the hypothesis test at the 5% level of significance for Toyota’s claim using the data above and determine the p-value. State your conclusion about the claim. Construct a 98% confidence interval for this study.

1.

2.

3.

4.

C. Based on your analysis of both claims from the makers of Pusho and Prius, what statement can be made about the miles per gallon of the two cars? Explain your reasoning.

Curtis & Company is an architectural firm specializing in home remodeling for private clients and new office buildings for corporate clients.

Curtis & Company charges customers at a billing rate equal to 130% of the client's total job cost. A client's total job cost is a combination of 1) professional cost based on the professional hours spent on the client's job, and 2) operating costs allocated to the client's job. Curtis currently allocates operating costs to jobs based on the number of professional hours spent on the job.

Curtis estimates its five professionals will work a total of 9,000 hours on client jobs during the year, and their salaries will total $990,000. All operating costs other than professional salaries (travel reimbursements, copy costs, secretarial salaries, office lease, etc.) can be grouped into three activities. Relevant information for these activities are estimated as follows:

Amy Lee hired Curtis & Company to design her kitchen remodeling. A total of 22 professional hours were spent on this job. In addition, Amy's remodeling job required one of the professionals to travel back and forth to her house for a total of 150 miles. The blueprints had to be copied five times because Amy changed the plans several times. In addition, 15 hours of secretarial time were used lining up the subcontractors for the job.

Question: What is the total cost of Amy Lee's remodeling job under the current single-driver system?

Question: What would be the total cost of Amy Lee's remodeling job under an activity-based costing system?

3. A package delivery service adopted a new dispatching system to try to reduce the total mileage required by its truck fleet to make deliveries. The new system would be worth the cost if it reduced the fleet mileage by more than 10% from its current level of 2200 miles per day. The miles required for each of the 66 days under a trial of the new system are recorded in column 1 of the Excel data file named “Package Delivery”. Using the given data and 7% level of significance, please conduct an appropriate test to determine if the new dispatching system is worth its cost. Based on your results, do you think the new system is worth its cost? Show the necessary steps and explain your conclusion