TABLE 16-6 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. \[\begin{array} { c c } \underline{ \text { Year } }&\underline{\text { Cases of Wine }} \\ { 1991 } & 270 \\ 1992 & 356 \\ 1993 & 398 \\ 1994 & 456 \\ 1995 & 358 \\ 1996 & 500 \\ 1997 & 410 \\ 1998 & 376 \end{array}\] -Referring to Table 16-6, a centered 3-year moving average is to be constructed for the wine sales. The moving average for 1995 is______ .

The answer of TABLE 16-6 The number of cases of merlot...

TABLE 16-3 The following table contains the number of complaints received in a department store for the first 6 months of last year. \[\begin{array} { l c } \underline{\text { Month }} &\underline{ \text { Complaints} } \\ \text { January } & 36 \\ \text { February } & 45 \\ \text { March } & 81 \\ \text { April } & 90 \\ \text { May } & 108 \\ \text { June } & 144 \end{array}\] -Referring to Table 16-3, if this series is smoothed using exponential smoothing with a smoothing constant of 1/3, how many terms would it have?

A) 4 B) 6 C) 5 D) 3 A) 4 B) 6 C) 5 D) 3

TABLE 16-12 The manager of a health club has recorded average attendance in newly introduced step classes over the last 15 months: 32.1, 39.5, 40.3, 46.0, 65.2, 73.1, 83.7, 106.8, 118.0, 133.1, 163.3, 182.8, 205.6, 249.1, and 263.5. She then used Microsoft Excel to obtain the following partial output for both a first- and second-order autoregressive model. SUMMARY OUTPUT - 2nd Order Model $\begin{array} { l r } \text { Regression Statistics}\\ \text { Multiple R } & 0.993 \\ \text { R Square } & 0.987 \\ \text { Adjusted R Square } & 0.985 \\ \text { Standard Error } & 9.276 \\ \text { Observations } & 15 \end{array}$ $\begin{array}{ll} & \text { Coetficients } \\ \text { Intercept } & 5.86 \\ \text { XVariable 1 } & 0.37 \\ \text { XVariable 2 } & 0.85 \end{array}$ $\text {SUMMARY}$ $\text {OUTPUT - 1st Order}$ $\text {Model Regression}$ $\begin{array} { l r } \text { Statistics}\\ \text { Multiple R } & 0.993 \\ \text { R Square } & 0.987 \\ \text { Adjusted R Square } & 0.985 \\ \text { Standard Error } & 9.150 \\ \text { Observations } & 15 \end{array}$ $\begin{array}{lc} & \text { Coefficients } \\ \text { Intercept } & 5.66 \\ \text { XVariable 1 } & 1.10 \\ \hline \end{array}$ -Referring to Table 16-12, using the second-order model, the forecast of average attendance for month 17 is _____.

The answer of TABLE 16-12 The manager of a...

TABLE 16-3 The following table contains the number of complaints received in a department store for the first 6 months of last year. \[\begin{array} { l c } \text { Month } & \text { Complaints } \\ \text { January } & 36 \\ \text { February } & 45 \\ \text { March } & 81 \\ \text { April } & 90 \\ \text { May } & 108 \\ \text { June } & 144 \end{array}\] -Referring to Table 16-3, if this series is smoothed using exponential smoothing with a smoothing constant of 1/3, what would be the third term?

A) 68 B) 81 C) 65.33 D) 53 A) 68 B) 81 C) 65.33 D) 53

TABLE 16-3 The following table contains the number of complaints received in a department store for the first 6 months of last year. \[\begin{array} { l c } \underline{\text { Month }} & \underline{\text { Complaints }} \\ \text { January } & 36 \\ \text { February } & 45 \\ \text { March } & 81 \\ \text { April } & 90 \\ \text { May } & 108 \\ \text { June } & 144 \end{array}\] -Referring to Table 16-3, if a three-term moving average is used to smooth this series, how many terms would it have?

A) 2 B) 4 C) 5 D) 3 A) 2 B) 4 C) 5 D) 3

TABLE 16-4 Given below are EXCEL outputs for various estimated autoregressive models for Coca-Cola's real operating revenues (in billions of dollars) from 1975 to 1998. From the data, we also know that the real operating revenues for 1996, 1997, and 1998 are 11.7909, 11.7757 and 11.5537, respectively. $\text { AR (1) Model: }$ $\begin{array}{lcccc} \hline & \text { Coeficients } & \text { Standard Error } & t \text { Stat } & p \text {-value } \\ \hline \text { Intercept } & 0.1802077 & 0.39797154 & 0.452815546 & 0.655325119 \\ \text { XLag1 } & 1.011222533 & 0.049685158 & 20.35260757 & 2.64373 \mathrm{E}-15 \end{array}$ $\text { AR (2)Model: }$ $\begin{array}{lcccc} \hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & p \text {-value } \\ \hline \text { Intercept } & 0.30047473 & 0.4407641 & 0.681713257 & 0.503646149 \\ \text { XLag1 } & 1.17322186 & 0.234737881 & 4.998008229 & 7.98541 \mathrm{E}-05 \\ \text { XLag2 } & 0.183028189 & 0.250716669 & -0.730020026 & 0.474283347 \end{array}$ $\text { AR (3) Model: }$ $\begin{array}{lrccc} \hline & \text { Coeficients } & \text { Standard Error } & t \text { Stat } & p \text {-value } \\ \hline \text { Interept } & 0.313043288 & 0.514437257 & 0.608515972 & 0.550890271 \\ \text { XLag1 } & 1.173719587 & 0.246490594 & 4.761721601 & 0.000180926 \\ \text { XLag2 } & -0.069378567 & 0.373086508 & -0.185958391 & 0.854678245 \\ \text { XLag3 } & -0.122123515 & 0.282031297 & -0.433014053 & 0.670448392 \end{array}$ -Referring to Table 16-4 and using a 5% level of significance, what is the appropriate AR model for Coca-Cola's real operating revenue?

A) AR(1) B) AR(2) C) AR(3) D) any of the above A) AR(1) B) AR(2) C) AR(3) D) any of the above

TABLE 16-4 Given below are EXCEL outputs for various estimated autoregressive models for Coca-Cola's real operating revenues (in billions of dollars) from 1975 to 1998. From the data, we also know that the real operating revenues for 1996, 1997, and 1998 are 11.7909, 11.7757 and 11.5537, respectively. $\text { AR (1) Model: }$ $\begin{array}{lcccc} \hline & \text { Coeficients } & \text { Standard Error } & t \text { Stat } & p \text {-value } \\ \hline \text { Intercept } & 0.1802077 & 0.39797154 & 0.452815546 & 0.655325119 \\ \text { XLag1 } & 1.011222533 & 0.049685158 & 20.35260757 & 2.64373 \mathrm{E}-15 \end{array}$ $\text { AR (2)Model: }$ $\begin{array}{lcccc} \hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & p \text {-value } \\ \hline \text { Intercept } & 0.30047473 & 0.4407641 & 0.681713257 & 0.503646149 \\ \text { XLag1 } & 1.17322186 & 0.234737881 & 4.998008229 & 7.98541 \mathrm{E}-05 \\ \text { XLag2 } & 0.183028189 & 0.250716669 & -0.730020026 & 0.474283347 \end{array}$ $\text { AR (3) Model: }$ $\begin{array}{lrccc} \hline & \text { Coeficients } & \text { Standard Error } & t \text { Stat } & p \text {-value } \\ \hline \text { Interept } & 0.313043288 & 0.514437257 & 0.608515972 & 0.550890271 \\ \text { XLag1 } & 1.173719587 & 0.246490594 & 4.761721601 & 0.000180926 \\ \text { XLag2 } & -0.069378567 & 0.373086508 & -0.185958391 & 0.854678245 \\ \text { XLag3 } & -0.122123515 & 0.282031297 & -0.433014053 & 0.670448392 \end{array}$ -Referring to Table 16-4, if one decides to use AR(3), what will the predicted real operating revenue for Coca-Cola be in 2001?

A) $11.84 billion B) $12.47 billion C) $11.68 billion D) $11.59 billion A) $11.84 billion B) $12.47 billion C) $11.68 billion D) $11.59 billion

Exam 16: Time-Series Forecasting and Index Numbers

TABLE 16-6 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. 1991 270 1992 356 1993 398 1994 456 1995 358 1996 500 1997 410 1998 376 -Referring to Table 16-6, a centered 3-year moving average is to be constructed for the wine sales. The moving average for 1995 is______ .

(Short Answer)

4.9/5

(35)

Question 41

TABLE 16-3 The following table contains the number of complaints received in a department store for the first 6 months of last year. January 36 February 45 March 81 April 90 May 108 June 144 -Referring to Table 16-3, if this series is smoothed using exponential smoothing with a smoothing constant of 1/3, how many terms would it have?

(Multiple Choice)

4.7/5

(45)

Question 42

TABLE 16-12 The manager of a health club has recorded average attendance in newly introduced step classes over the last 15 months: 32.1, 39.5, 40.3, 46.0, 65.2, 73.1, 83.7, 106.8, 118.0, 133.1, 163.3, 182.8, 205.6, 249.1, and 263.5. She then used Microsoft Excel to obtain the following partial output for both a first- and second-order autoregressive model. SUMMARY OUTPUT - 2nd Order Model Regression Statistics Multiple R 0.993 R Square 0.987 Adjusted R Square 0.985 Standard Error 9.276 Observations 15 Coetficients Intercept 5.86 XVariable 1 0.37 XVariable 2 0.85 $\text {SUMMARY}$ $\text {OUTPUT - 1st Order}$ $\text {Model Regression}$ Statistics Multiple R 0.993 R Square 0.987 Adjusted R Square 0.985 Standard Error 9.150 Observations 15 Coefficients Intercept 5.66 XVariable 1 1.10 -Referring to Table 16-12, using the second-order model, the forecast of average attendance for month 17 is _____.

(Short Answer)

4.8/5

(41)

Question 43

TABLE 16-6 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. 1991 270 1992 356 1993 398 1994 456 1995 358 1996 500 1997 410 1998 376 -Referring to Table 16-6, exponential smoothing with a weight or smoothing constant of 0.4 will be used to smooth the wine sales. The value of E₅, the smoothed value for 1995 is _____.

(Short Answer)

4.9/5

(51)

Question 44

TABLE 16-15 Given below are the prices of a basket of four food items from 1996 to 2000. Year Wheat (\ / Bushel ) Corn (\ / Bushel ) Soybeans (\ / Bushel ) Milk (\ / hundredweight) 1996 4.25 3.71 7.41 15.03 1997 3.43 27 7.55 13.63 1998 2.63 23 6.05 15.18 1999 2.11 1.97 4.68 14.72 2000 2.16 1.9 4.81 12.32 -Referring to Table 16-15, what are the simple price indexes for wheat, corn, soybeans and milk, respectively, in 1996 using 2000 as the base year?

(Short Answer)

4.8/5

(41)

Question 45

Which of the following methods should not be used for short-term forecasts into the future?

(Multiple Choice)

4.8/5

(27)

Question 46

TABLE 16-7 The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48. -Referring to Table 16-7, the number of arrivals will be smoothed with a 3-term moving average. The first smoothed value will be ______.

(Short Answer)

4.7/5

(38)

Question 47

TABLE 16-14 Given below are the average prices for three types of energy products in the United States from 1992 to 1995. Year Electricity N atural Gas Fuel Oil 1992 43.205 25.893 0.892 1993 16.959 28.749 0.969 1994 47.202 28.933 1.034 1995 48.874 29.872 0.913 1996 48.693 28.384 0.983 -Referring to Table 16-14, what is the Laspeyres price index for the group of three energy items in 1995 for a family that consumed 15 units of electricity, 24 units of natural gas and 200 units of fuel oil in 1992 using 1992 as the base year?

(Short Answer)

4.8/5

(33)

Question 48

TABLE 16-3 The following table contains the number of complaints received in a department store for the first 6 months of last year. Month Complaints January 36 February 45 March 81 April 90 May 108 June 144 -Referring to Table 16-3, if this series is smoothed using exponential smoothing with a smoothing constant of 1/3, what would be the third term?

(Multiple Choice)

4.7/5

(35)

Question 49

TABLE 16-6 The number of cases of merlot wine sold by a Paso Robles winery in an 8-year period follows. 1991 270 1992 356 1993 398 1994 456 1995 358 1996 500 1997 410 1998 376 -Referring to Table 16-6, a centered 3-year moving average is to be constructed for the wine sales. The result of this process will lead to a total of _____moving averages.

(Short Answer)

4.8/5

(37)

Question 50

TABLE 16-3 The following table contains the number of complaints received in a department store for the first 6 months of last year. January 36 February 45 March 81 April 90 May 108 June 144 -Referring to Table 16-3, if a three-term moving average is used to smooth this series, how many terms would it have?

(Multiple Choice)

4.9/5

(30)

Question 51

TABLE 16-11 Business closures in Laramie, Wyoming from 1989 to 1994 were: 1993 10 1994 11 1995 13 1996 19 1997 24 1998 35 Microsoft Excel was used to fit both first-order and second-order autoregressive models, resulting in the following partial outputs: $\begin{array} { |l c |}\hline\text {SUMMARY OUTPUT- 2 ^ { \text {nd } } Order Model}\\& \text {Coefficients}\\ \text { Intercept } & - 5.77 \\ \text { XVariable 1 } & 0.80 \\ \text { XVariable 2 } & 1.14\\\\ \text {SUMMARY OUTPUT- 1st Order Model}\\& \text {Coefficients}\\ \text {Intercept }&- 4.16\\ \text {XVariable 1 }& 1.59\\\hline \end{array}$ -Referring to Table 16-11, the residuals for the second-order autoregressive model are, , , and _.

(Short Answer)

4.8/5

(42)

Question 52

TABLE 16-7 The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48. -Referring to Table 16-7, the number of arrivals will be exponentially smoothed with a smoothing constant of 0.25. The forecast of the number of arrivals on the seventh Monday will be ______ .

(Short Answer)

4.9/5

(39)

Question 53

TABLE 16-5 A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the 3-year period from 1996 to 1998. The following is the resulting regression equation: ln Y^{^}= 3.37 + 0.117 X - 0.083 Q₁ + 1.28 Q₂ + 0.617 Q₃ where Y^{^}is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 1996. Q₁ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise. Q₂ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise. Q₃ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise. -Referring to Table 16-5, using the regression equation, which of the following values is the best forecast for the number of contracts in the second quarter of 2000?

(Multiple Choice)

4.9/5

(34)

Question 54

TABLE 16-15 Given below are the prices of a basket of four food items from 1996 to 2000. Wheat Corn Soybeans Milk Year ( \/ Bushel) ( \/ Bushel) ( \/ Bushel) ( \/ hundredweight) 1996 4.25 3.71 7.41 15.03 1997 3.43 27 7.55 13.63 1998 2.63 23 6.05 15.18 1999 2.11 1.97 4.68 14.72 2000 2.16 1.9 4.81 12.32 -Referring to Table 16-15, what is the Paasche price index for the basket of four food items in 2000 that consisted of 40 bushels of wheat, 50 bushels of corn, 35 bushels of soybeans and 60 hundredweight of milk in 2000 using 1996 as the base year?

(Short Answer)

4.9/5

(40)

Question 55

TABLE 16-15 Given below are the prices of a basket of four food items from 1996 to 2000. Year Wheat (\ / Bushel ) Corn (\ / Bushel ) Soybeans (\ / Bushel ) Milk (\ / hundredweight) 1996 4.25 3.71 7.41 15.03 1997 3.43 27 7.55 13.63 1998 2.63 23 6.05 15.18 1999 2.11 1.97 4.68 14.72 2000 2.16 1.9 4.81 12.32 -Referring to Table 16-15, what are the simple price indexes for wheat, corn, soybeans and milk, respectively, in 1999 using 1996 as the base year?

(Short Answer)

4.8/5

(32)

Question 56

TABLE 16-7 The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48. -Referring to Table 16-7, the number of arrivals will be smoothed with a 3-term moving average. The last smoothed value will be _____.

(Short Answer)

4.8/5

(34)

Question 57

TABLE 16-4 Given below are EXCEL outputs for various estimated autoregressive models for Coca-Cola's real operating revenues (in billions of dollars) from 1975 to 1998. From the data, we also know that the real operating revenues for 1996, 1997, and 1998 are 11.7909, 11.7757 and 11.5537, respectively. $\text { AR (1) Model: }$ Coeficients Standard Error t Stat p -value Intercept 0.1802077 0.39797154 0.452815546 0.655325119 XLag1 1.011222533 0.049685158 20.35260757 2.64373-15 $\text { AR (2)Model: }$ Coefficients Standard Error t Stat p -value Intercept 0.30047473 0.4407641 0.681713257 0.503646149 XLag1 1.17322186 0.234737881 4.998008229 7.98541-05 XLag2 0.183028189 0.250716669 -0.730020026 0.474283347 $\text { AR (3) Model: }$ Coeficients Standard Error t Stat p -value Interept 0.313043288 0.514437257 0.608515972 0.550890271 XLag1 1.173719587 0.246490594 4.761721601 0.000180926 XLag2 -0.069378567 0.373086508 -0.185958391 0.854678245 XLag3 -0.122123515 0.282031297 -0.433014053 0.670448392 -Referring to Table 16-4 and using a 5% level of significance, what is the appropriate AR model for Coca-Cola's real operating revenue?

(Multiple Choice)

4.7/5

(34)

Question 58

TABLE 16-4 Given below are EXCEL outputs for various estimated autoregressive models for Coca-Cola's real operating revenues (in billions of dollars) from 1975 to 1998. From the data, we also know that the real operating revenues for 1996, 1997, and 1998 are 11.7909, 11.7757 and 11.5537, respectively. $\text { AR (1) Model: }$ Coeficients Standard Error t Stat p -value Intercept 0.1802077 0.39797154 0.452815546 0.655325119 XLag1 1.011222533 0.049685158 20.35260757 2.64373-15 $\text { AR (2)Model: }$ Coefficients Standard Error t Stat p -value Intercept 0.30047473 0.4407641 0.681713257 0.503646149 XLag1 1.17322186 0.234737881 4.998008229 7.98541-05 XLag2 0.183028189 0.250716669 -0.730020026 0.474283347 $\text { AR (3) Model: }$ Coeficients Standard Error t Stat p -value Interept 0.313043288 0.514437257 0.608515972 0.550890271 XLag1 1.173719587 0.246490594 4.761721601 0.000180926 XLag2 -0.069378567 0.373086508 -0.185958391 0.854678245 XLag3 -0.122123515 0.282031297 -0.433014053 0.670448392 -Referring to Table 16-4, if one decides to use AR(3), what will the predicted real operating revenue for Coca-Cola be in 2001?

(Multiple Choice)

4.9/5

(30)

Question 59

TABLE 16-14 Given below are the average prices for three types of energy products in the United States from 1992 to 1995. Year Electricity N atural Gas Fuel Oil 1992 43.205 25.893 0.892 1993 16.959 28.749 0.969 1994 47.202 28.933 1.034 1995 48.874 29.872 0.913 1996 48.693 28.384 0.983 -Referring to Table 16-14, what is the Paasche price index for the group of three energy items in 1996 for a family that consumed 13 units of electricity, 26 units of natural gas and 235 units of fuel oil in 1996 using 1992 as the base year?

(Short Answer)

4.9/5

(37)

Question 60

Which of the following methods should not be used for short-term forecasts into the future?

TABLE 16-7 The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48. -Referring to Table 16-7, the number of arrivals will be smoothed with a 3-term moving average. The first smoothed value will be ______.

TABLE 16-7 The number of passengers arriving at San Francisco on the Amtrak cross-country express on 6 successive Mondays were: 60, 72, 96, 84, 36, and 48. -Referring to Table 16-7, the number of arrivals will be smoothed with a 3-term moving average. The last smoothed value will be _____.

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions and Sampling

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Two-Sample Tests

Analysis of Variance

Chi-Square Tests and Nonparametric Tests

Simple Linear Regression

Introduction to Multiple Regression

Multiple Regression Model Building

Decision Making

Statistical Applications in Quality Management

Statistical Analysis Scenarios and Distributions

Filters