The average cost per night of a hotel room in New York City is $210. Assume this estimate is based on a sample of 15 hotels and that the sample standard deviation is $20. a) What is the point estimate of the population mean? b) With 90% confidence, what is the margin of error? c) What is the 95% confidence interval estimate of the population mean?
The average cost per night of a hotel room in New York City is $210. Assume this estimate is based on a sample of 15 hotels and that the sample standard deviation is $20. a) What is the point estimate of the population mean? b) With 90% confidence, what is the margin of error? c) What is the 95% confidence interval estimate of the population mean?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Q4) The average cost per night of a hotel room in New York City is $210. Assume this estimate is based on a sample of 15 hotels and that the sample standard deviation is $20.
a) What is the point estimate of the population
b) With 90% confidence, what is the margin of error?
c) What is the 95% confidence
d) Calculate good samples and bad samples and show the area of these two samples using a curve based on finding c).
e) Write a summary based on your answer of c)
Transcribed Image Text:CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION
Cumulative
probability
Entries in the table
give the area under the
curve to the left of the
z value. For example, for
z = 1.25, the cumulative
probability is .8944.
.00
.01
.02
.03
.04
.05
.06
.07
.08
09
5040
.5080
.5120
.5199
.5596
.0
5000
.5160
.5239
.5279
5319
5359
5438
.5832
.5478
.5871
.5557
.5948
.6331
.1
5398
.5517
5636
.5675
.5714
5753
.2
.3
5910
.6293
.6664
.5793
$987
.6368
.6736
.6026
.6064
.6443
6103
.6141
.6217
.6591
.6179
.6255
.6628
.6406
.6480
.6517
.4
.6554
.6700
.6772
.6808
.6844
.6879
.5
.7088
.6950
.7291
.7611
.6915
.6985
.7019
.7054
.7123
.7157
.7190
4כרה
.7357
.7673
.7967
,7389
.7486
.7794
.6
.7257
.7580
.7881
.7324
.7422
.7454
.7517
.7549
.7
.7823
.8106
.8365
.7642
.7704
.7734
.7764
.7852
.7910
.7939
7995
.8078
.8340
.8
8023
8051
8133
.9
8159
.8186
.8212
.8238
.8264
.8289
.8315
8389
.8413
.8643
.8849
.8438
.8665
.8869
.8485
.8708
1.0
.8461
8554
.8508
.8729
.8925
.8531
.8577
.8599
8621
1.1
.8686
.8888
.8749
8770
.8790
.8810
.8830
1.2
.8907
.8944
.8962
.8980
.8997
.9032
.9192
.9049
.9207
9099
9251
9115
9265
9131
9279
.9162
9306
.9015
9177
9319
1.3
.9066
.9082
9147
1.4
.9222
9236
9292
.9345
.9357
9474
1.5
.9332
.9370
.9484
.9582
.9382
9406
.9429
.9535
.9625
9441
.9545
.9394
.9418
.9525
.9616
.9693
L6
.9452
9505
9515
9463
.9564
9649
9495
9554
.9641
1.9
1.7
.9573
9591
9599
.9608
9633
1.8
.9656
.9664
.9671
.9678
.9686
9699
9706
.9713
.9719
.9726
.9732
.9738
.9744
9750
.9756
9761
.9767
.9783
.9788
.9793
9838
.9798
9842
.9803
.9846
9808
.9812
.9854
2.0
כ977.
.9778
.9817
.9857
.9890
2.1
.9821
.9826
9830
9834
9850
2.2
9875
.9904
.9861
.9864
.9868
.9871
.9878
.9881
.9884
9887
.9893
.9918
2.3
.9896
.9898
.9901
.9906
.9911
.9913
.9934
.9909
.9916
2.4
9920
.9922
.9925
.9927
.9929
.9931
9932
9936
.9940
.9943
.9945
9959
.9969
.9946
9960
.9970
2.5
.9938
9953
.9941
.9951
9963
.9948
.9949
.9952
2.6
9955
9956
9957
.9968
.9961
.9962
.9964
9965
.9974
.9967
.9976
2.7
.9972
.9979
.9973
.9980
9966
.9971
.9974
2.8
.9975
.9977
.9977
.9978
.9979
.9981
2.9
.9981
.9982
.9982
.9983
.9984
.9984
.9985
.9985
.9986
.9986
3.0
.9987
.9987
.9987
.9988
.9988
.9989
.9989
.9989
9990
.9990
Transcribed Image Text:Table entry for p and C is
the critical value t with
probability p lying to its
right and probability C lying
between -t' and t'.
Probability p
TABLE D
t distribution critical values
Upper-tail probability p
dí
.25
.20
.15
.10
.05
.025
.02
.01
.005
.0025
.001
0005
1.000
1.376
1.061
0.978
1.963
1.386
1.250
1.190
1.156
3.078
1.886
1.638
6.314
2.920
2.353
12.71
4,303
3.182
2.776
2.571
15.89
4.849
3.482
2.999
2.757
31.82
6.965
4.541
3.747
3.365
63.66
9.925
5.841
4.604
127.3
14.09
7.453
5.598
4.773
318.3
22.33
10.21
7.173
5.893
5.208
4.785
4.501
4.297
4.144
4.025
3.930
3.852
3.787
3.733
0.816
0.765
0.741
0.727
636.6
31.60
12.92
8.610
3
0.941
0.920
0.906
0.896
0.889
0.883
0.879
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
0.718
0.711
0.706
0.703
4.032
3.707
3.499
3.355
3.250
3.169
6.869
5.959
5.408
5.041
1.134
1.119
1.108
1.100
1.093
1.088
1.083
1.079
1.076
1.074
1.071
2.447
2.365
2.306
2.262
2,612
2.517
2.449
2.398
2.359
2.328
2.303
2.282
2.264
2.249
2.235
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
4.317
4.029
3.833
3.690
3.581
3.497
8
9.
4.781
4.587
10
0.700
0.697
2.228
2.201
2.179
11
12
13
14
15
0.876
0.873
0.870
0.868
3.106
3.055
4.437
0.695
0.694
0.692
0.691
0.690
0.689
3.428
3.372
3.326
3.286
4.318
4.221
4.140
2.160
2.145
2.131
2.120
2.110
3.012
2.977
2.947
2.921
0.866
0.865
0.863
0.862
0.861
0.860
0.859
0.858
0.858
0.857
4.073
4.015
3.965
3.922
3.883
16
3.252
3.222
3.197
3.174
3.153
3.135
3.119
3.686
3.646
3.611
3.579
3.552
17
1.069
1.067
1.066
1.064
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.740
1.734
1.729
1.725
1.721
1,717
1.714
2.224
2.214
2.898
2.878
2.861
2.845
2.831
2.819
18
19
20
0.688
0.688
0.687
0.686
0.686
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.552
2.539
2.528
2.518
2.508
2,205
2.197
2.189
2.183
21
22
1.063
1.061
1.060
1.059
3.527
3.505
3.485
3.467
3.450
3.850
3.819
3.792
3.768
3.745
23
24
25
0.685
0.685
2.177
2.172
2.167
2.162
2.158
2.154
2.150
2.147
2.123
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.423
2.403
2.390
2.374
2.364
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
1.711
1.708
1.706
1.703
3.104
3.091
3.078
3.067
3.057
3.047
0.684
0.856
0.856
0.855
0.855
0.854
0.854
0.851
1.058
1.058
1.057
1.056
1.055
3.725
3.707
3.690
3.674
3.659
3.646
26
27
28
0.684
0.684
1.315
1.314
1.313
0.683
0.683
0.683
2.052
2.048
2.045
2.042
2.021
3.435
3.421
3.408
3.396
3.385
1.701
1.699
29
30
40
50
60
80
1.311
1.310
1.303
1.299
1.296
1.292
1.290
1.282
1.055
1.050
1.047
3.038
3.030
2.971
2.937
1.697
0.681
0.679
0.679
0.678
0.677
0.675
0.674
1.684
2.704
2.678
2.660
2.639
3.307
0.849
0.848
0.846
0.845
3.551
3.496
3.460
3.416
3.390
3.300
3.291
1.676
1.671
1.664
2.009
2.000
1.990
2.109
2.099
2.088
2.081
3.261
1.045
2.915
2.887
3.232
3.195
3.174
1.043
100
1.042
1.037
1.036
1.660
1.646
1.984
2.626
2.581
2,576
2.871
2.813
2.807
1000
0.842
0.841
1.962
2.056
2.054
2.330
2.326
3.098
3.091
1.282
1.645
1.960
50%
60%%
70%
80%
90%
95%
96e
98%
99%
99.5%
99.8%
99.9%
Confidence level C
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