[meteor_slideshow slideshow=”arp1″]
Notes:
1. Before doing this assignment, do the practice problem posted under Apply and Discover.
2. Word-process your solutions within this template. Do not create a new file.
3. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.
4. Word-process formulas using Equation Editor and diagrams using Drawing Tool.
Problem 1
Annual family dental expenses for the families of a random sample of ten employees of a company are given below. You can assume the family dental expenses for the employees of the company are normally distributed.
$450, $390, $550, $140, $690, $600, $250, $330, $490, $810
a) Compute the mean and standard deviation of the sample.
b) Determine the point estimate and 95% confidence interval for the mean family dental expenses of all employees of the company.
c) Interpret the confidence interval.
d) How would you communicate this information to the Vice-President of Human Resources in non-statistical language.
e) How could this information be used in negotiations with the dental insurer of the company in setting the premiums for the next year.
Problem 2
The average price of regular gasoline in the continental US states and the District of Columbia was $3.74 on August 18, 2008. Alaska and Hawaii are not included as the gas prices there are much higher than the continental US. The price of gasoline in the eleven western states of the U.S. on the same day is given below. Test the hypothesis that the average price of gasoline in the western states is higher than the national average for Continental USA and the District of Columbia, i.e., higher than $3.74. Use level of significance = 0.05.
California $4.04
Arizona $3.72
Colorado $3.83
Idaho $4.01
Montana $3.97
Nevada $3.84
New Mexico $3.77
Oregon $3.92
Utah $4.04
Washington $3.99
Wyoming $3.90
Reference: Daily Fuel Gauge Report. (n.d.). Retrieved August 18, 2008, from AAA: http://fuelgaugereport.opisnet.com/sbsavg.html
Notes: Before doing this assignment, do the practice problem posted under Apply and Discover. Use the instructions given in the document “Using Excel for Regression Analysis” for doing scatter plot, inserting the trend line and producing the regression report using the data analysis regression tool. Copy and paste the scatter plot and the regression report from Excel into this document. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.
Problem 3
Data for a sample of houses sold recently in the suburb of a large metropolis are given below:
Area of House (hundreds of square feet) Selling Price (thousands of dollars)
20 250
19 220
27 350
28 390
30 320
15 200
25 360
23 290
18 210
35 410
(a) Do a scatter diagram for the data, insert the trend line and add the equation and R2 value to the diagram.
(b) Find SSxx, SSyy and SSxy.
(c) Determine the correlation coefficient. Comment on the value of the correlation coefficient.
(d) Find the regression equation manually. Compare with the equation obtained when doing the scatter diagram.
(e) Find SST, SSR and SSE.
(f) Find the degrees of freedom associated with the sum of squares in part (e).
(g) Find MSR and MSE.
(h) Summarize your findings as an ANOVA table.
(i) Find the coefficient of determination R2.
(j) Find standard error of the estimate se
(k) Test the hypothesis that Y and X are not related. That is, test H0: 1 = 0 vs. H1: 1 0 by using a t-statistic. Use = 0.05.
(l) Find the predicted value of Y given X = 24. Give an interpretation of the predicted value in the context of the problem.
(m) Find a 95% confidence interval for the mean value of Y given X = 24. Give an interpretation of the confidence interval in the context of the problem.
Notes: Before doing this assignment, do the practice problem posted under Apply and Discover. Word-process your answers within this document. Do not create a new file. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.
Problem 4
A group of legislators wanted to look at factors that affect the number of traffic fatalities. They collected some data for 1994 from the National Transportation Safety Board on the number of fatalities for 50 states and the District of Columbia (DC), the number of licensed drivers, the number of registered vehicles, and the number of vehicle miles traveled.
State Traffic Fatalities Licensed Drivers (thousands) Registered Vehicles (thousands) Vehicle Miles Traveled (millions)
AL 1083 3043 3422 48956
AK 85 443 508 4150
AZ 903 2654 2980 38774
AR 610 1770 1560 24948
CA 4226 20359 23518 271943
CO 585 2620 3144 33705
CT 310 2205 2638 27138
DE 112 512 568 7025
DC 69 366 270 3448
FL 2687 10885 10132 121989
GA 1426 4666 5638 82822
HI 122 742 781 7935
ID 249 779 1062 11652
IL 1554 7548 8331 92316
IN 974 3834 4850 62108
IA 478 1921 2929 25737
KS 442 1794 1965 24678
KY 778 2498 2615 39822
LA 838 2606 3242 37430
ME 188 916 1071 12469
MD 651 3311 3543 44165
MA 440 4209 3956 46990
MI 1419 6602 7599 85183
MN 644 2668 3869 43317
MS 791 1659 2056 28548
MO 1089 3512 4179 57288
MT 202 536 967 9116
NE 271 1154 1490 15466
NV 294 987 983 13019
NH 119 878 1013 10501
NJ 761 5521 5752 60466
NM 447 1162 1472 20480
NY 1658 10444 10428 112970
NC 1431 4779 5462 71928
ND 88 443 687 6338
OH 1371 7722 9647 98200
OK 687 2363 2863 36980
OR 490 2401 2748 29453
PA 1441 8146 8557 92347
RI 63 682 728 7095
SC 847 2458 2764 37245
SD 154 512 845 7631
TN 1214 3583 5150 54524
TX 3186 12012 13287 178348
UT 342 1203 1381 18078
VT 77 435 502 6152
VA 930 4631 5593 67609
WA 638 3741 4654 47428
WV 356 1317 1375 17112
WI 712 3542 4044 50273
WY 144 354 583 6689
Source: Statistical Abstract of the United States 1996
(Reference: Pelosi and Sadifer, Doing Statistics for Business with Excel, Second Edition)
(a) Copy and paste the data from this document to an Excel file. Select the Number of Traffic Fatalities as the dependent variable. Do a scatter plot between the Number of Traffic Fatalities and Number of licensed drivers (in thousands), a second scatter plot between the Number of Traffic Fatalities and the Number of Registered Vehicles (in thousands) and a third scatter plot between the Number of Traffic Fatalities and the Number of Vehicle Miles Traveled (in millions). Paste the scatter plots below and discuss the nature of the relationship based on the scatter plots. Note: Follow the instructions given in module 4 to do the scatter plots.
(b) Select the Number of Traffic Fatalities as the dependent variable and the Number of licensed drivers (in thousands), the Number of Registered Vehicles (in thousands) and the Number of Vehicle Miles Traveled (in millions) as independent variables. Conduct multiple regression using Excel. Paste the output report below. Note: Follow the instructions given in module 4 to conduct simple regression. At the step where you specify the input data range, instead of selecting the data for one independent variable, select data for all the independent variables.
(c) Write the equation from the regression output report. If you are using symbols in the equation for the variables, do define the symbols before using the symbols in the equation. Provide clear and complete interpretation of the coefficients b1, b2 and b3 in the equation. There is no need to interpret b0.
(d) What is the value of R2 for this model? Do you think that the model does a good job of explaining the variation in the number of traffic fatalities? Why or why not?
(e) Set up the hypotheses to test whether the model is significant. Is the regression model significant at 0.05 as the level of significance? What does this mean?
(f) Set up the hypotheses to test for each of the regression coefficients individually and perform the test at the 0.05 level of significance.
(g) What are your conclusions from the tests on individual coefficients? Do any variables need to be dropped? If so, rerun the regression and determine the final regression equation. Note: drop the variables one at a time starting with the variable with the largest p-value (least significant), rerun the regression without the data for the dropped variable, check the p-values again and continue the process until all p-values (other than for the intercept term) are less than the level of significance.
(h) Compare the final equation with the first regression equation. What recommendations do you have about using the final equation? Give reasons for your answer.
(i) Suppose there was a state with the following values of the independent variables: Number of Licensed Drivers (in thousands) = 3,500, Number of Registered Vehicles (in thousands) = 4,000 and Number of Vehicle Miles Traveled (in millions) = 45,000. Determine and interpret the predicted value of the number of traffic fatalities.
Notes: Before doing this assignment, do the practice problem posted under Apply and Discover. Word-process your answers within this document. Do not create a new file. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.
Problem 5
The U.S. Census Bureau publishes data on factory orders for all manufacturing, durable goods, and nondurable goods industries. Shown here are factory orders in the United States from 1987 through 1999 ($ billion).
(a) Use these data to develop forecasts for the years 1992 through 1999 using a 5-year moving average.
(b) Use these data to develop forecasts for the years 1992 through 1999 using a 5-year weighted moving average. Weight the most recent year by 6, the previous year by 4, the year before that by 2, and the other years by 1.
(c) Which method is more suitable for forecasting factory orders? Hint: Compare the two methods based on Mean Absolute Deviation (MAD)?
Year Factory Orders ($ billion)
1987 2,512.7
1988 2,739.2
1989 2,874.9
1990 2,934.1
1991 2,865.7
1992 2,978.5
1993 3,092.4
1994 3,356.8
1995 3,607.6
1996 3,749.3
1997 3,952.0
1998 3,949.0
1999 4,137.0
(Black, Ken (2006). Business Statistics (4th ed. update). John Wiley & Sons, New York, NY. Page 615)
Problem 6
The following data list worldwide shipments of personal computers (in thousands) according to Dataquest.
Year Shipments (in thousands)
1990 23,738
1991 26,966
1992 32,411
1993 38,851
1994 47,894
1995 60,171
1996 71,065
1997 82,400
1998 97,321
(a) Use exponential smoothing to determine the forecast of shipments for the year 1999. Use the actual shipments for 1990 as the starting forecast for 1991. Use a smoothing constant of = 0.4.
(b) Plot the data, fit a trend line, and discuss the strength of prediction of the regression model.
(c) Use the regression model to predict the shipments for the year 1999.
(d) Compare the two forecasts. Which forecast would you prefer to use and why?
(Adapted from: Black, Ken (2006). Business Statistics (4th ed. update). John Wiley & Sons, New York, NY. Page 622)
[meteor_slideshow slideshow=”arp2″]
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