3. (20 points) Bill plans to put his home on the market for sale. However, he wants to estimate the price he may get from the sale. He collected data on home prices, land area, size of the home in square feet, and the age of the home, all in a comparable neighbourhood. The table below gives the data. Price of the House (in thousands of dollars) Land Area (in acres) Size of the House (Square feet) Age of the House (years) 455 1.4 2500 8 278 .9 2250 12 463 1.8 2900 5 327 .7 1800 9 505 2.6 3200 4 264 1.2 2400 28 445 2.1 2700 9 346 1. 2050 13 487 2.8 2850 7 289 1.6 2400 16 434 3.2 2600 5 411 1.7 2300 8 223 .5 1700 19 a. Write the population regression model and indicate the whether you expect a positive or negative relationship between the dependent variable and each of the independent variables. b. Using Minitab, find the regression of price on land area, house size, and age. c. Write the estimated regression equation. d. What percentage of the total variation in house prices is explained by the independent variables? e. Construct a 95 per cent confidence interval for the coefficient of age. f. "Do " independent variables significantly affect the house price at a 5% level of significance? Give reasons for your answer. g. Bill's 2000 square feet house sits on a 2-acre and is 10 years old. How much can he expect from the sale of his house?

4. (20 points) a. In an analysis of variable, what do the sum of squares within (SSW) and the sum of squares between (SSB or SSG) mean. - Explain. Why is it that a one-way analysis of variance is always an upper-tail test? b. What are the disadvantages of an unweighted price index? What is done to avoid these disadvantages? c. What are the components of a time series? Give a brief narrative on each of these components.

5. (20 points) The following data shows prices of three types of fruits over ten years. Year Mango Orange Blackberry 1 50 100 150 2 55 115 155 3 60 100 125 4 55 110 130 5 63 120 120 6 65 110 125 7 70 105 140 8 75 120 170 9 60 130 160 10 65 135 175 Take year 1 as the base year. In that year, Mango, Orange, and Blackberry production were 50, 25, and 15 thousand kilograms, respectively. a) Find the un-weighted index of prices. b) Find the Laspeyres index for fruit prices. c) What is the change in price from year 6 to year 7 if you use an unweighted index. d) What is the change in price from year 6 to year 7 if you use the Laspeyres index. e) Is the answer to c is different from the answer to d. Explain your answer.

6. (20 points) Three suppliers provide 500 one-gram packets of saffron per shipment to a departmental store. Random samples of six shipments from each of the three suppliers - Shujon Traders, Lavender, Just Quality -- were carefully checked, and the number of packets not conforming to the quality specifications is counted. These numbers are listed in the table below. Shujon Traders Lavender Just Quality 28 22 33 37 27 29 34 29 39 29 20 33 31 18 37 33 30 38 At .05 level of significance, test the hypothesis that population mean several packets per shipment not meeting the quality specification are the same for all three suppliers.

Charges of +2q, +q, and -q are distributed in an area as shown in figure. Consider a Gaussian surface located around the +2q charge, with a point P located on the surface as shown. Which of -29 the statements below is true? 0-9 The electric field is the same everywhere inside the Gaussian surface. The net electric field at point P can be determined using the Gaussian surface shown. The net flux through the Gaussian surface depends only on the +2q charge. The electric field at P depends only on the +2g charge The electric field is the same everywhere on the Gaussian surfaceAnswer given is b and c but I think electric field will be constant Consider a spherically symmetric charge distribution centred at origin, Variation of electric flux with an imaginary Gaussian surface of radius r centre at origin is given by $ = $or3. (A) Electric field in space lying in Gaussian surface is uniform (B) The volume charge density in space lying in Gaussian surface is uniform (C) For a given radius of spherical Gaussian surface the electric flux does not depend on position of centre of Gaussian surface () For a given radius of spherical Gaussian surface the electric flux depends on position of centre of Gaussian surface uniform volume charge density p on inner cylinder and uniform surface charge 's) and radius of outer cylinder is 'b', It is found thatQ22.1 The figure shows a Gaussian A 22 surface with rectangular sides and positive point charge to at its center. If all the dimensions of the Gaussian surface double, but charge 1 g remains at its center, the electric flux through the surface will A. increase by a factor of 4. B. increase by a factor of 2. C. remain the same, D. decrease by a factor of 1/2. E. decrease by a factor of 1/4. Q22.2 Spherical Gaussian surface #1 has point charge to at its center. Spherical Gaussian surface #2, of the same size, also encloses the charge but is not centered on it. There are no other charges inside either Gaussian surface. Compared to the electric flux through surface #1, the flux through surface #2 is A. greater. B. the same. C. less, but not zero. D. zero. Gaussian Gaussian surface #1 surface #2 E, Not enough information is given to decide.2. A spherical Gaussian surface of radius r surrounds a positive point charge with charge Q as shown. Points A and B lie on the Gaussian surface. a. [4 pts] In terms of the given variables, find the net flux through the Gaussian surface. b. [4 pts] Is the potential difference OV = (VB-VA) positive, negative, or zero? Explain. c. [4 pts] A neutral metal sphere is brought near the Gaussian surface as shown. Does the net flux through the Gaussian surface increase, decrease, or remain the same? Explain. [4] Metal sphere d. [4 pts] The neutral metal sphere is now moved so that part of it is enclosed by the Gaussian surface as shown. i. , Does the magnitude of the net flux through the Gaussian surface increase, decrease, or remain the same? Explain. +0 ii. [4 pts] Does the magnitude of the electric potential difference (VB-VA) increase, decrease, or remain the same? Explain. Metal sphere