Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, noshows are costly, and they would rather have their staff focused on customer service rather than maintaining a reservation system (pressherald.com). However, it is important to be able to give reasonable estimates of waiting time when customers arrive and put their name on the waiting list. The file RestaurantLine contains 10 observations of number of people in line ahead of a customer (independent variable x) and actual waiting time (dependent variable y). The estimated regression equation is: ŷ=11.97+7.68x and MSE=144.2066. Use Table 2 of Appendix B. a. Develop a point estimate for a customer who arrive with three people on the wait-list (to 1 decimal). b. Develop a confidence interval for the mean waiting time for a customer who arrives with three customers already in line (to 2 decimals). c. Develop a prediction interval for Roger
Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, noshows are costly, and they would rather have their staff focused on customer service rather than maintaining a reservation system (pressherald.com). However, it is important to be able to give reasonable estimates of waiting time when customers arrive and put their name on the waiting list. The file RestaurantLine contains 10 observations of number of people in line ahead of a customer (independent variable x) and actual waiting time (dependent variable y). The estimated regression equation is: ŷ=11.97+7.68x and MSE=144.2066. Use Table 2 of Appendix B. a. Develop a point estimate for a customer who arrive with three people on the wait-list (to 1 decimal). b. Develop a confidence interval for the mean waiting time for a customer who arrives with three customers already in line (to 2 decimals). c. Develop a prediction interval for Roger
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, noshows are costly, and they would rather have their staff focused on customer service rather than maintaining a reservation system (pressherald.com). However, it is important to be able to give reasonable estimates of waiting time when customers arrive and put their name on the waiting list. The file RestaurantLine contains 10 observations of number of people in line ahead of a customer (independent variable x) and actual waiting time (dependent variable y). The estimated regression equation is: ŷ=11.97+7.68x and MSE=144.2066. Use Table 2 of Appendix B.
a. Develop a point estimate for a customer who arrive with three people on the wait-list (to 1 decimal).
b. Develop a confidence interval for the mean waiting time for a customer who arrives with three customers already in line (to 2 decimals).
c. Develop a prediction interval for Roger and Sherry Davy's waiting time if there are three customers in line when they arrive (to 2 decimals).
Transcribed Image Text:Number of Customers Waiting Time (Minutes)
4
58
3
38
5
37
45
7
63
4
42
8
83
4
54
7
70
5
29
Transcribed Image Text:TABLE 2 t DISTRIBUTION
Area or
probability Entries in the table give t values for an
area or probability in the upper tail of the t
distribution, For example, with 10 degrees
of freedom
fom and a .05 area in the upper tail,
tor = 1812
Area in Upper Tail
Degrees
of Freedom
.20
10
05
.025
.01
.005
1.376
6.314
2.706
31.821
63.656
9 925
3.078
12.700
4.303
1.061
1.886
2.920
6.965
978
1.638
2.353
3.182
4.541
5.841
.941
1.533
2.132
2.776
3.747
4.604
920
1.476
2.015
2.571
3.365
4 032
906
1.440
1.943
2.447
3.143
3.707
.896
1.415
1.895
2.365
2.998
3.499
3.355
3.250
.889
1.397
1.860
2.306
2.896
.883
1.383
1.833
2.262
2.821
879
1 372
1,812
3.169
2228
2.764
1.796
1782
3.106
3.055
.876
1.363
1 356
2.201
2.718
873
2.179
2.681
1.771
2.650
3.012
2 077
870
1.350
2.160
.868
1.345
1 761
2 145
2.624
866
1.753
2.947
1241
2131
2.602
1.746
1.740
2.921
2.898
.865
1.337
2.120
2.583
.863
1.333
2.110
2.567
862
1.330
1.734
2.101
2.552
2.878
861
1.328
1.729
2.093
2.539
2.861
TABLE 2 t DISTRIBUTION (Continued)
Area in Upper Tail
Degrees
of Freedom
20
.10
.05
025
.01
005
1.690
1.688
852
1.306
1 306
1 305
2.030
2.438
2.724
852
2.028
2.434
2.719
1.687
2.026
2.715
2.712
851
2.431
851
1.304
1.686
2.024
2.429
.851
1.304
1.685
2.023
2.426
2.708
.851
1.303
1.684
2.021
2.423
2.704
.850
850
1.303
1.683
2.020
2.421
2.701
1.302
1.682
2.018
2.418
2.698
2 605
.850
1.302
1.681
2.017
2.416
.850
1.301
1.680
2.015
2.414
2.692
2.690
2.687
2.685
850
1.301
1.679
2.014
2.412
850
1.300
1.679
2.013
2.410
849
1.300
1.678
2.012
2.408
2.682
2.680
849
1.299
1.677
2.011
2.407
.849
1.299
1.677
2.010
2.405
849
1.299
1.676
2.009
2.403
2.678
2.676
2.674
2.672
849
1.298
1.675
2.008
2.402
849
1.298
1.675
2.007
2.400
848
1.298
1.674
2.006
2.399
.848
1.297
1 297
1.674
2.005
2 397
2670
1 207
2.668
848
1.673
2.004
2.396
1 297
1 297
1 296
.848
1.673
2.003
2.395
2.667
1.672
2.665
2.663
848
2.002
2.394
848
1.672
2.002
2.392
.848
1.296
1.671
2.001
2.391
2.662
1 296
1 296
2.660
2.659
848
1.671
2.000
2.390
848
1.670
2.000
2.389
847
1.295
1.670
1.999
2.388
2.657
1.998
2.656
2.655
847
1.295
1.669
2.387
.847
1.295
1.669
1.998
2.386
847
1.295
1.669
1.997
2.385
2.654
.847
1.295
1.668
1.997
2.384
2.652
847
1.294
1.668
1.996
2.383
2.651
.847
1.294
1.668
1.995
2.382
2.650
847
1.294
1.667
1.995
2.382
2.649
TABLE 2 I DISTRIBUTION (Continued)
Area in Upper Tail
Degrees
of Freedom
.20
10
.05
025
.01
,005
846
1.292
1.664
1.990
2.374
2.639
.846
1.292
1.664
1.990
2.373
2.638
846
1.292
1664
1.989
2.373
2.637
846
1.292
2,636
1663
1.005
1.663
1.989
2.372
.846
1.292
1.989
2.372
2.636
846
1 292
1.663
1 988
2.371
2,635
2.634
2.634
2.633
846
1.291
1.663
1.988
2.370
846
1.663
1.988
2.370
846
1.662
1.987
2.369
.846
1.662
1.987
2.369
2.632
846
1.662
1.987
2.368
2.632
846
1.662
1.986
2.368
2.631
846
1.662
1.986
2.368
2.630
846
1.661
1.986
2.367
2.630
.845
1.661
1.986
2.367
2.629
845
1.291
1.661
1.985
2.366
2.629
.845
1.290
1.661
1.985
2.366
2.628
845
2.627
1.290
1 290
1 290
1.661
1.985
1 984.
2.365
2.627
2.626
.845
1.661
2.365
.845
1.660
1.984
2.364
.845
1.290
1.660
1.984
2.364
2.626
842
1.282
1.645
1.960
2326
2.576
3%印的的 导子44手 4导导等令 另云纪3科 的%沉的的的d的d 的的何83
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