1) Find the uncertainty in kinetic energy. Kinetic energy depends on mass and velocity according to this function E(m,v) = 1/2 m v². Your measured mass and velocity have the following uncertainties     2.58 kg and   0.36 m/s. What is is the uncertainty in energy,  , if the measured mass, m = 4.75 kg and the measured velocity, v = -3.76 m/s? Units are not needed in your answer

2)Find the uncertainty in kinetic energy. Kinetic energy depends on mass and velocity according to this function E(m,v) = 1/2 m v². Your measured mass and velocity have the following uncertainties     0.47 kg and   2.48 m/s. What is is the uncertainty in energy,  , if the measured mass, m = 3.95 kg and the measured velocity, v = -22.69 m/s? Units are not needed in your answer.

3) The propagation of uncertainty formula for the equation y = ax^2 is

where ,and  . and . The values  and  are the uncertainties on a and x respectively.

If a = -4.5 +/- 0.4 and x = -4.7+/-0.7 then what is the uncertainty on y

4) After a million measurements of thing x, we find a sample mean of 60.45 and standard deviation of 3.24. What chance, in percent (0-100) does the next measurement have of being outside 3 standard deviations from the mean? Do not include the percent sign.

5) Find the uncertainty in a calculated average speed from the measurements of distance and time. Average speed depends on distance and time according to this function v(t,x) = x/t. Your measured distance and time have the following values and uncertainties x = 5.1 meters,   2.8 meters and t = 9.1 seconds and  0.2 seconds. What is the uncertainty in the average speed,  ? Units are not needed in your answer.

1. The waiting times​ (in minutes) of a random sample of 21 people at a bank have a sample standard deviation of 3.5 minutes. Construct a confidence interval for the population variance sigma squared and the population standard deviation sigma. Use a 99 % level of confidence. Assume the sample is from a normally distributed population. What is the confidence interval for the population variance sigma squared​?

2.You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals. A random sample of 55 home theater systems has a mean price of ​$113.00. Assume the population standard deviation is ​$15.20.

Question 1:- A potential investor collected attendance data over a period of 49 days at the North Mall and South Mall theaters in order to determine the difference between the average daily attendances. The North Mall Theater averaged 720 patrons per day with a variance of 100, while the South Mall Theater averaged 700 patrons per day with a variance of 96. Develop an interval estimate for the difference between the average daily attendances at the two theaters. Use a confidence coefficient of 0.95.

Question 2:-Zip, Inc. manufactures Zip drives on two different manufacturing processes. Because the management of this company is interested in determining if process 1 takes less manufacturing time, they selected independent random samples from each process. The results of the samples are shown below. (20 points)

                                          Process 1          Process 2

Sample size                               27               22

Sample mean (in minutes) 10              14

Sample variance                 16             25

1. State the null and alternative hypotheses.

2. Determine the degrees of freedom for the t-test.

3. Compute the test statistic

4. At 95% confidence, test to determine if there is sufficient evidence to indicate that process 1 takes a significantly shorter time to manufacture the Zip drives.

Question 3:-  

Shown below is a portion of computer output for a regression analysis relating to Y (dependent variable) and X (independent variable). (20 points)

ANOVA     

                  df SS

Regression   1 115.064

Residual 13   82.936

Total    

            Coefficients Standard Error

Intercept 15.532                 1.457

x              -1.106               0.261

a. Perform a t-test using the p-value approach and determine whether x and y are related. Let α = .05.

b. Using the p-value approach, perform an F test, and determine whether x and y are related.

c. Compute the coefficient of determination and fully interpret its meaning. Be specific.

Question 1:- A potential investor collected attendance data over a period of 49 days at the North Mall and South Mall theaters in order to determine the difference between the average daily attendances. The North Mall Theater averaged 720 patrons per day with a variance of 100, while the South Mall Theater averaged 700 patrons per day with a variance of 96. Develop an interval estimate for the difference between the average daily attendances at the two theaters. Use a confidence coefficient of 0.95.

Question 2:-Zip, Inc. manufactures Zip drives on two different manufacturing processes. Because the management of this company is interested in determining if process 1 takes less manufacturing time, they selected independent random samples from each process. The results of the samples are shown below. (20 points)

                                          Process 1          Process 2

Sample size                               27               22

Sample mean (in minutes) 10              14

Sample variance                 16             25

1. State the null and alternative hypotheses.

2. Determine the degrees of freedom for the t-test.

3. Compute the test statistic

4. At 95% confidence, test to determine if there is sufficient evidence to indicate that process 1 takes a significantly shorter time to manufacture the Zip drives.

Question 3:-  

Shown below is a portion of computer output for a regression analysis relating to Y (dependent variable) and X (independent variable). (20 points)

ANOVA     

                  df SS

Regression   1 115.064

Residual 13   82.936

Total    

            Coefficients Standard Error

Intercept 15.532                 1.457

x              -1.106               0.261

a. Perform a t-test using the p-value approach and determine whether x and y are related. Let α = .05.

b. Using the p-value approach, perform an F test, and determine whether x and y are related.

c. Compute the coefficient of determination and fully interpret its meaning. Be specific.

A regional airline transfers passengers from small airports to a larger regional hub airport. The airline data analyst was assigned to estimate the revenue ( in thousands of dollars) generated by each of the 22 small airports based on two variables: the distance from each airport ( in miles) to the hub and the population ( in hundreds) of the cities in which each of the 22 airports is located. The data is given in the following table.

Airport revenue         distance         population

1          233                 233                 56

2          272                 209                 74

3          253                 206                 74

4          296                 232                 78

5          268                 125                 73

6          296                 245                 54

7          276                 213                 100

8          235                 134                 98

9          253                 140                 95       

10        233                 165                 81

11        240                 234                 52

12        267                 205                 96

13        338                 214                 96       

14        243                 183                 73

15        252                 230                 55

16        269                 238                 91

17        242                 144                 64

18        233                 220                 60

19        234                 170                 60

20        450                 170                 240    

21        340                 290                 70

22        200                 340                 75                   

1. Using PROC CORR in SAS, create a matrix of scatter plots for revenue, population, and distance. Include this graph in your LATEX document.
2. From your scatter plots in part (a), is there a data point that you think may be an “issue” for analysis?
   
3. Construct and report a multiple regression model relating :
             revenue (y)
            distance (x1)
            population (x2)
             using SAS.
   
4. Construct the 95% confidence interval for β1 by hand. (Use βˆ1 and the standard error calculated by SAS.)

a) The point at which a company's costs equal its revenues is the break-even point. C represents the cost, in dollars, of x units of a product and R represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even. That is, find the value of x for which C=R.

C=15x+32,000 and R=17x.

How many units must be produced and sold in order to break even?

b) A bicycle travels at a speed of 55 miles per hour for x hours. Find an expression for the distance that the bicycle travels.

c) The price per unit, p, and the demand, x, for a particular material is related by the linear equation p =140 -7/8 X, while the supply is given by the linear equation

p=7/8x. At what value of p does supply equal demand?

d) Suppose that a cyclist began a 476 mi ride across a state at the western edge of the state, at the same time that a car traveling toward it leaves the eastern end of the state. If the bicycle and car met after

8.5 hr and the car traveled 32.2 mph faster than the bicycle, find the average rate of each.

The car's average rate is

The bicycle's average rate is

e) A baseball team has home games on Thursday and Saturday. The two games together earn $4640.00 for the team. Thursday 's game generates$300.00 less than Saturday 's

game. How much money was taken in at each game? How much money did Thursday 's game generate? How much money did Saturday 's game generate?

Bill has just returned from a duck hunting trip. He brought home eight ducks. Bill’s friend, John, disapproves of duck hunting, and to discourage Bill from further hunting, John presented him with the following cost estimate per duck: Camper and equipment: Cost, $15,000; usable for eight seasons; 12 hunting trips per season $ 156 Travel expense (pickup truck): 100 miles at $0.39 per mile (gas, oil, and tires—$0.28 per mile; depreciation and insurance—$0.11 per mile) 39 Shotgun shells (two boxes per hunting trip) 25 Boat: Cost, $2,080, usable for eight seasons; 12 hunting trips per season 22 Hunting license: Cost, $80 for the season; 12 hunting trips per season 7 Money lost playing poker: Loss, $36 (Bill plays poker every weekend whether he goes hunting or stays at home) 36 Bottle of whiskey: Cost, $25 per hunting trip (used to ward off the cold) 25 Total cost $ 310 Cost per duck ($310 ÷ 8 ducks) $ 39 Required: 1. Assuming the duck hunting trip Bill has just completed is typical, what costs are relevant to a decision as to whether Bill should go duck hunting again this season? 2. Suppose Bill gets lucky on his next hunting trip and shoots 12 ducks using the same amount of shotgun shells he used on his previous hunting trip to bag 8 ducks. How much would it have cost him to shoot the last two ducks?

A real estate investor wants to study the relationship between annual return on his commer- cial retail shops (measured in thousands of dollars) as it relates to their location and the number of homes near the shops. Specifically, the investor has collected data on the annual return of the shops, the number of households within 15 miles of the shops (measured in thousands), and the location of the shops (whether the shops are in a suburban area, near a shopping mall, or downtown). The annual return data can be found in the file “RealEstate.csv” in the d2l. As demonstrated in the lecture, please create a subset data of size 18 and perform your statistical analysis for the subset data. Please note that the subset data should be a random sample of the given data.

(a) State the mean of the response.
(b) Is the multiple linear regression model useful for prediction? Show details. Use ? = 0.05. (c) Provide the detailed interpretations of b1, b2, and b3 in the context of the problem.

(d) Use your estimated regression equation to predict the annual return for a shop in mall with 120,000 households near the shop.

Shop. Annual Return($1000s). Number of Households(1000s). Location.
3 245.81   232   Mall
4   137.07   108   Mall
5   207.36   220   Suburban
6   146.12   150   Suburban
8   188.19   198   Suburban
9   152.23   149   Downtown
10   182.23   192   Suburban
11   198.88   179   Mall
13   156.22   130   Mall
15   195.62   199   Downtown
16   210.38   224   Suburban
17   209.16   215   Downtown
18   260.82   250   Mall
20   127.66   129   Suburban
22   219.93   203   Mall
23   166.61   166   Downtown
27   219.67   227   Downtown
29   232.32   217   Mall

Should you video conference or travel to a business meeting?

1. Suppose you own a profitable small business in Washington, D.C. You desire to hold an essential 1-hour meeting with business executives in New York, NY. You have two options:
2. You can fly to New York. You own 25,000 frequent-flyer miles, which you can return to the airline at any time for a free ticket anywhere in the United States. Thus, you need not pay for your flight to New York. Your only expenditures would be for 15-minute cab rides to and from the airport in D.C. (fares = $25 each way) plus 15-minute cab rides to and from the airport in New York (fares = $25 each way). Or,
3. You can use a video conferencing facility. Last January, you paid $3,000 to obtain access to a video conferencing facility located within your office building for one year. You also must pay $125/hour for each hour the facility is used.

You estimate the meeting will be equally effective (the benefit is assumed to be the same) if held in person or via video conferencing. What option should you choose and why? How should you think about this decision? Make sure to calculate both the implicit and explicit costs of both options. You don’t need to make any additional assumptions other than those given in this scenario to make your decisions. Please also pay attention to the sunk cost that may complicate your decision. Therefore, review the concept of sunk cost very carefully before you complete your post.