STATS Misc. Questions 10.55, 10.59, 11.21, 11.22, 11.26, 12.3, 12.7, 12.9, 12.19, 12.21
Question # 00060217
Posted By:
Updated on: 04/09/2015 12:08 AM Due on: 04/09/2015
10.55 Consider an experiment with four groups, with eight values in each. For the ANOVA summary table below, fill in all the missing results:
Source Degrees of Freedom Sum of Squares Mean Square (Variance) F
Among groups c – 1 =? SSA=? MSA=80 Fstat?
Within groups n – c = ? SSW=560 MSW= ?
Total n – 1= ? SST=?
10.59 A hospital conducted a study of the waiting time in its emergency room. The hospital has a main campus and three satellite locations. Management had a business objective of reducing waiting time for emergency room cases that did not require immediate attention. To study this, a random sample of 15 emergency room cases that did not require immediate attention at each location were selected on a particular day, and the waiting time (measured from check-in to when the patient was called into the clinic area) was measured.
The results are stored in ERWaiting .
Main Satellite 1 Satellite 2 Satellite 3
120.08 30.75 75.86 54.05
81.90 61.83 37.88 38.82
78.79 26.40 68.73 36.85
63.83 53.84 51.08 32.83
79.77 72.30 50.21 52.94
47.94 53.09 58.47 34.13
79.88 27.67 86.29 69.37
48.63 52.46 62.90 78.52
55.43 10.64 44.84 55.95
64.06 53.50 64.17 49.61
64.99 37.28 50.68 66.40
53.82 34.31 47.97 76.06
62.43 66.00 60.57 11.37
65.07 8.99 58.37 83.51
81.02 29.75 30.40 39.17
a. At the 0.05 level of significance, is there evidence of a difference in the mean waiting times in the four locations?
b. If appropriate, determine which locations differ in mean waiting time.
c. At the 0.05 level of significance, is there evidence of a difference in the variation in waiting time among the four locations?
11.21 When performing a X^2 test of independence in a contingency table with r rows and c columns, determine the upper-tail critical value of the test statistic in each of the following circumstances:
? = 0.05, r = 4 rows, c = 5 columns
? = 0.01, r = 4 rows, c = 5 columns
? = 0.01, r = 4 rows, c = 6 columns
? = 0.01, r = 3 rows, c = 6 columns
? = 0.01, r = 6 rows, c = 3 columns
11.22 The owner of a restaurant serving Continental-style entrees has the business objective of learning more about the patterns of patron demand during the Friday-to-Sunday weekend time period. Data were collected from 630 customers on the type of entrée ordered and the type of dessert ordered and organized into the following table:
TYPE OF
DESSERT
TYPE OF ENTRÉE
Beef Poultry Fish Pasta Total
Ice cream 13 8 12 14 47
Cake 98 12 29 6 145
Fruit 8 10 6 2 26
None 124 98 149 41 412
Total 243 128 196 63 630
At the 0.05 level of significance, is there evidence of a
relationship between type of dessert and type of entrée?
11.26 USA Today reported on when the decision of
what to have for dinner is made. Suppose the results were
based on a survey of 1,000 respondents and considered
whether the household included any children under 18
years old. The results are cross-classified in the following
table:
When Decision Made One Adult/No Children Two or More Adults/Children Two or More Adults/No Children
Just before eating 162 54 154
In the afternoon 73 38 69
In the morning 59 58 53
A few days before 21 64 45
The night before 15 50 45
Always eat the same thing on this night 2 16 2
Not sure 7 6 7
At the 0.05 level of significance, is there evidence of a significant relationship between when the decision is made of what to have for dinner and the type of household?
12.3 Fitting a straight line to a set of data yields the following prediction line:
Y ?_t = 16 – 0.5X_t
Interpret the meaning of the Y intercept, b_0
Interpret the meaning of the slope, b_1
Predict the value of Y for X = 6.
12.7 Starbucks Coffee Co. uses a data-based approach to improving the quality and customer satisfaction of its products.
When survey data indicated that Starbucks needed to improve its package sealing process, an experiment was conducted (data extracted from L. Johnson and S. Burrows, “For Starbucks, It’s In the Bag,” Quality Progress, March 2011, pp. 17–23) to determine the factors in the bag-sealing equipment that might be
affecting the ease of opening the bag without tearing the inner liner of the bag. One factor that could affect the rating of the ability of the bag to resist tears was the plate gap on the bagsealing equipment. Data was collected on 19 bags in which the plate gap was varied. The results are stored in Starbucks.
Tear Viscosity Pressure Plate Gap
0.00 350.00 180.00 0.00
0.00 350.00 170.00 0.00
0.45 319.00 186.00 1.80
0.85 380.00 174.00 1.80
0.35 350.00 180.00 0.00
0.30 300.00 180.00 0.00
0.70 400.00 180.00 0.00
1.90 350.00 190.00 0.00
0.25 350.00 180.00 0.00
0.10 319.00 186.00 -1.80
0.15 380.00 186.00 -1.80
3.90 350.00 180.00 3.00
0.00 380.00 174.00 -1.80
0.55 350.00 180.00 0.00
0.00 350.00 180.00 -3.00
0.05 319.00 174.00 -1.80
0.40 319.00 174.00 1.80
4.30 380.00 186.00 1.80
0.00 350.00 180.00 0.00
a. Construct a scatter plot.
b. Assuming a linear relationship, use the least-squares method to determine the regression coefficients b_0 and b_1
c. Interpret the meaning of the slope, b_1, in this problem.
d. Predict the tear rating when the plate gap is equal to 0.
12.9 An agent for a residential real estate company has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data (stored
in Rent ).
Rent Size
950 850
1600 1450
1200 1085
1500 1232
950 718
1700 1485
1650 1136
935 726
875 700
1150 956
1400 1100
1650 1285
2300 1985
1800 1369
1400 1175
1450 1225
1100 1245
1700 1259
1200 1150
1150 896
1600 1361
1650 1040
1200 755
800 1000
1750 1200
a. Construct a scatter plot.
b. Use the least-squares method to determine the regression coefficients b_0 and b_1.
c. Interpret the meaning of b_0 and b_1 in this problem.
d. Predict the monthly rent for an apartment that has 1,000 square feet.
12.19 In Problem 12.7 on page 441, you used the plate gap on the bag-sealing equipment to predict the tear rating of a bag of coffee (stored in Starbucks). Using the results of that problem,
Tear Viscosity Pressure Plate Gap
0.00 350.00 180.00 0.00
0.00 350.00 170.00 0.00
0.45 319.00 186.00 1.80
0.85 380.00 174.00 1.80
0.35 350.00 180.00 0.00
0.30 300.00 180.00 0.00
0.70 400.00 180.00 0.00
1.90 350.00 190.00 0.00
0.25 350.00 180.00 0.00
0.10 319.00 186.00 -1.80
0.15 380.00 186.00 -1.80
3.90 350.00 180.00 3.00
0.00 380.00 174.00 -1.80
0.55 350.00 180.00 0.00
0.00 350.00 180.00 -3.00
0.05 319.00 174.00 -1.80
0.40 319.00 174.00 1.80
4.30 380.00 186.00 1.80
0.00 350.00 180.00 0.00
a. determine the coefficient of determination, r^2, and interpret its meaning.
b. determine the standard error of the estimate.
c. How useful do you think this regression model is for predicting the tear rating based on the plate gap in the bag-sealing equipment?
12.21 In Problem 12.9 on page 442, an agent for a real estate company wanted to predict the monthly rent for apartments, based on the size of the apartment (stored in Rent).
Source Degrees of Freedom Sum of Squares Mean Square (Variance) F
Among groups c – 1 =? SSA=? MSA=80 Fstat?
Within groups n – c = ? SSW=560 MSW= ?
Total n – 1= ? SST=?
10.59 A hospital conducted a study of the waiting time in its emergency room. The hospital has a main campus and three satellite locations. Management had a business objective of reducing waiting time for emergency room cases that did not require immediate attention. To study this, a random sample of 15 emergency room cases that did not require immediate attention at each location were selected on a particular day, and the waiting time (measured from check-in to when the patient was called into the clinic area) was measured.
The results are stored in ERWaiting .
Main Satellite 1 Satellite 2 Satellite 3
120.08 30.75 75.86 54.05
81.90 61.83 37.88 38.82
78.79 26.40 68.73 36.85
63.83 53.84 51.08 32.83
79.77 72.30 50.21 52.94
47.94 53.09 58.47 34.13
79.88 27.67 86.29 69.37
48.63 52.46 62.90 78.52
55.43 10.64 44.84 55.95
64.06 53.50 64.17 49.61
64.99 37.28 50.68 66.40
53.82 34.31 47.97 76.06
62.43 66.00 60.57 11.37
65.07 8.99 58.37 83.51
81.02 29.75 30.40 39.17
a. At the 0.05 level of significance, is there evidence of a difference in the mean waiting times in the four locations?
b. If appropriate, determine which locations differ in mean waiting time.
c. At the 0.05 level of significance, is there evidence of a difference in the variation in waiting time among the four locations?
11.21 When performing a X^2 test of independence in a contingency table with r rows and c columns, determine the upper-tail critical value of the test statistic in each of the following circumstances:
? = 0.05, r = 4 rows, c = 5 columns
? = 0.01, r = 4 rows, c = 5 columns
? = 0.01, r = 4 rows, c = 6 columns
? = 0.01, r = 3 rows, c = 6 columns
? = 0.01, r = 6 rows, c = 3 columns
11.22 The owner of a restaurant serving Continental-style entrees has the business objective of learning more about the patterns of patron demand during the Friday-to-Sunday weekend time period. Data were collected from 630 customers on the type of entrée ordered and the type of dessert ordered and organized into the following table:
TYPE OF
DESSERT
TYPE OF ENTRÉE
Beef Poultry Fish Pasta Total
Ice cream 13 8 12 14 47
Cake 98 12 29 6 145
Fruit 8 10 6 2 26
None 124 98 149 41 412
Total 243 128 196 63 630
At the 0.05 level of significance, is there evidence of a
relationship between type of dessert and type of entrée?
11.26 USA Today reported on when the decision of
what to have for dinner is made. Suppose the results were
based on a survey of 1,000 respondents and considered
whether the household included any children under 18
years old. The results are cross-classified in the following
table:
When Decision Made One Adult/No Children Two or More Adults/Children Two or More Adults/No Children
Just before eating 162 54 154
In the afternoon 73 38 69
In the morning 59 58 53
A few days before 21 64 45
The night before 15 50 45
Always eat the same thing on this night 2 16 2
Not sure 7 6 7
At the 0.05 level of significance, is there evidence of a significant relationship between when the decision is made of what to have for dinner and the type of household?
12.3 Fitting a straight line to a set of data yields the following prediction line:
Y ?_t = 16 – 0.5X_t
Interpret the meaning of the Y intercept, b_0
Interpret the meaning of the slope, b_1
Predict the value of Y for X = 6.
12.7 Starbucks Coffee Co. uses a data-based approach to improving the quality and customer satisfaction of its products.
When survey data indicated that Starbucks needed to improve its package sealing process, an experiment was conducted (data extracted from L. Johnson and S. Burrows, “For Starbucks, It’s In the Bag,” Quality Progress, March 2011, pp. 17–23) to determine the factors in the bag-sealing equipment that might be
affecting the ease of opening the bag without tearing the inner liner of the bag. One factor that could affect the rating of the ability of the bag to resist tears was the plate gap on the bagsealing equipment. Data was collected on 19 bags in which the plate gap was varied. The results are stored in Starbucks.
Tear Viscosity Pressure Plate Gap
0.00 350.00 180.00 0.00
0.00 350.00 170.00 0.00
0.45 319.00 186.00 1.80
0.85 380.00 174.00 1.80
0.35 350.00 180.00 0.00
0.30 300.00 180.00 0.00
0.70 400.00 180.00 0.00
1.90 350.00 190.00 0.00
0.25 350.00 180.00 0.00
0.10 319.00 186.00 -1.80
0.15 380.00 186.00 -1.80
3.90 350.00 180.00 3.00
0.00 380.00 174.00 -1.80
0.55 350.00 180.00 0.00
0.00 350.00 180.00 -3.00
0.05 319.00 174.00 -1.80
0.40 319.00 174.00 1.80
4.30 380.00 186.00 1.80
0.00 350.00 180.00 0.00
a. Construct a scatter plot.
b. Assuming a linear relationship, use the least-squares method to determine the regression coefficients b_0 and b_1
c. Interpret the meaning of the slope, b_1, in this problem.
d. Predict the tear rating when the plate gap is equal to 0.
12.9 An agent for a residential real estate company has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data (stored
in Rent ).
Rent Size
950 850
1600 1450
1200 1085
1500 1232
950 718
1700 1485
1650 1136
935 726
875 700
1150 956
1400 1100
1650 1285
2300 1985
1800 1369
1400 1175
1450 1225
1100 1245
1700 1259
1200 1150
1150 896
1600 1361
1650 1040
1200 755
800 1000
1750 1200
a. Construct a scatter plot.
b. Use the least-squares method to determine the regression coefficients b_0 and b_1.
c. Interpret the meaning of b_0 and b_1 in this problem.
d. Predict the monthly rent for an apartment that has 1,000 square feet.
12.19 In Problem 12.7 on page 441, you used the plate gap on the bag-sealing equipment to predict the tear rating of a bag of coffee (stored in Starbucks). Using the results of that problem,
Tear Viscosity Pressure Plate Gap
0.00 350.00 180.00 0.00
0.00 350.00 170.00 0.00
0.45 319.00 186.00 1.80
0.85 380.00 174.00 1.80
0.35 350.00 180.00 0.00
0.30 300.00 180.00 0.00
0.70 400.00 180.00 0.00
1.90 350.00 190.00 0.00
0.25 350.00 180.00 0.00
0.10 319.00 186.00 -1.80
0.15 380.00 186.00 -1.80
3.90 350.00 180.00 3.00
0.00 380.00 174.00 -1.80
0.55 350.00 180.00 0.00
0.00 350.00 180.00 -3.00
0.05 319.00 174.00 -1.80
0.40 319.00 174.00 1.80
4.30 380.00 186.00 1.80
0.00 350.00 180.00 0.00
a. determine the coefficient of determination, r^2, and interpret its meaning.
b. determine the standard error of the estimate.
c. How useful do you think this regression model is for predicting the tear rating based on the plate gap in the bag-sealing equipment?
12.21 In Problem 12.9 on page 442, an agent for a real estate company wanted to predict the monthly rent for apartments, based on the size of the apartment (stored in Rent).
Using the results of that problem,
Rent Size
950 850
1600 1450
1200 1085
1500 1232
950 718
1700 1485
1650 1136
935 726
875 700
1150 956
1400 1100
1650 1285
2300 1985
1800 1369
1400 1175
1450 1225
1100 1245
1700 1259
1200 1150
1150 896
1600 1361
1650 1040
1200 755
800 1000
1750 1200
a. determine the coefficient of determination, r^2, and interpret its meaning.
b. determine the standard error of the estimate.
c. How useful do you think this regression model is for predicting the monthly rent?
d. Can you think of other variables that might explain the variation in monthly rent?
Rent Size
950 850
1600 1450
1200 1085
1500 1232
950 718
1700 1485
1650 1136
935 726
875 700
1150 956
1400 1100
1650 1285
2300 1985
1800 1369
1400 1175
1450 1225
1100 1245
1700 1259
1200 1150
1150 896
1600 1361
1650 1040
1200 755
800 1000
1750 1200
a. determine the coefficient of determination, r^2, and interpret its meaning.
b. determine the standard error of the estimate.
c. How useful do you think this regression model is for predicting the monthly rent?
d. Can you think of other variables that might explain the variation in monthly rent?
-
Rating:
/5
Solution: STATS Chapter 10, 11 & 12 Questions Solution