The absolute viscosity for sunflower oil is supposed to average 0.0311 Pa⋅s at 38 ∘C. Suppose a food scientist collects a random sample of 4 quantities of sunflower oil and computes the mean viscosity for his sample to be x¯=0.0318 Pa⋅s at 38 ∘C. Assume that measurement errors are normally distributed and that the population standard deviation of sunflower oil viscosity is known to be σ=0.0009 Pa⋅s. The scientist will use a one‑sample z‑test for a mean, at a significance level of α=0.01, to evaluate the null hypothesis, H0:μ=0.0311 Pa⋅s against the alternative hypothesis, H1:μ≠0.0311 Pa⋅s. Complete the scientist's analysis by calculating the value of the one-sample z‑statistic, the p‑value, and then deciding whether to reject the null hypothesis. First, compute the z‑statistic, z. Provide your answer precise to two decimal places. Avoid rounding within calculations. z= Determine the P-value of the test using either a table of standard normal critical values or software. Give your answer precise to four decimal places. P=
The absolute viscosity for sunflower oil is supposed to average 0.0311 Pa⋅s at 38 ∘C. Suppose a food scientist collects a random sample of 4 quantities of sunflower oil and computes the mean viscosity for his sample to be x¯=0.0318 Pa⋅s at 38 ∘C. Assume that measurement errors are normally distributed and that the population standard deviation of sunflower oil viscosity is known to be σ=0.0009 Pa⋅s. The scientist will use a one‑sample z‑test for a mean, at a significance level of α=0.01, to evaluate the null hypothesis, H0:μ=0.0311 Pa⋅s against the alternative hypothesis, H1:μ≠0.0311 Pa⋅s. Complete the scientist's analysis by calculating the value of the one-sample z‑statistic, the p‑value, and then deciding whether to reject the null hypothesis. First, compute the z‑statistic, z. Provide your answer precise to two decimal places. Avoid rounding within calculations. z= Determine the P-value of the test using either a table of standard normal critical values or software. Give your answer precise to four decimal places. P=
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
I need help with these two questions. Here are the data table if needed.
The absolute viscosity for sunflower oil is supposed to average 0.0311 Pa⋅s at 38 ∘C. Suppose a food scientist collects a random sample of 4 quantities of sunflower oil and computes the
The scientist will use a one‑sample z‑test for a mean, at a significance level of α=0.01, to evaluate the null hypothesis, H0:μ=0.0311 Pa⋅s against the alternative hypothesis, H1:μ≠0.0311 Pa⋅s. Complete the scientist's analysis by calculating the value of the one-sample z‑statistic, the p‑value, and then deciding whether to reject the null hypothesis.
First, compute the z‑statistic, z. Provide your answer precise to two decimal places. Avoid rounding within calculations.
z=
Determine the P-value of the test using either a table of standard normal critical values or software. Give your answer precise to four decimal places.
P=
Transcribed Image Text:2.60
0.99534
0.99547
0.99560
0.99573
0.99585
0.99598
0.99609
0.99621
0.99632
0.99643
2.70
0.99653
0.99664
0.99674
0.99683
0.99693
0.99702
0.99711
0.99720
0.99728
0.99736
2.80
0.99744
0.99752
0.99760
0.99767
0.99774
0.99781
0.99788
0.99795
0.99801
0.99807
2.90
0.99813
0.99819
0.99825
0.99831
0.99836
0.99841
0.99846
0.99851
0.99856
0.99861
3.00
0.99865
0.99869
0.99874
0.99878
0.99882
0.99886
0.99889
0.99893
0.99896
0.99900
3.10
0.99903
0.99906
0.99910
0.99913
0.99916
0.99918
0.99921
0.99924
0.99926
0.99929
3.20
0.99931
0.99934
0.99936
0.99938
0.99940
0.99942
0.99944
0.99946
0.99948
0.99950
3.30
0.99952
0.99953
0.99955
0.99957
0.99958
0.99960
0.99961
0.99962
0.99964
0.99965
3.40
0.99966
0.99968
0.99969
0.99970
0.99971
0.99972
0.99973
0.99974
0.99975
0.99976
3.50
0.99977
0.99978
0.99978
0.99979
0.99980
0.99981
0.99981
0.99982
0.99983
0.99983
3.60
0.99984
0.99985
0.99985
0.99986
0.99986
0.99987
0.99987
0.99988
0.99988
0.99989
3.70
0.99989
0.99990
0.99990
0.99990
0.99991
0.99991
0.99992
0.99992
0.99992
0.99992
3.80
0.99993
0.99993
0.99993
0.99994
0.99994
0.99994
0.99994
0.99995
0.99995
0.99995
3.90
0.99995
0.99995
0.99996
0.99996
0.99996
0.99996
0.99996
0.99996
0.99997
0.99997
4.00
0.99997
0.99997
0.99997
0.99997
0.99997
0.99997
0.99998
0.99998
0.99998
0.99998
Transcribed Image Text:Table values represent cumulative area under curve to left of z score
Second decimal place in z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-4.00
0.00003
0.00003
0.00003
0.00003
0.00003
0.00003
0.00002
0.00002
0.00002
0.00002
-3.90
0.00005
0.00005
0.00004
0.00004
0.00004
0.00004
0.00004
0.00004
0.00003
0.00003
-3.80
0.00007
0.00007
0.00007
0.00006
0.00006
0.00006
0.00006
0.00005
0.00005
0.00005
3.70
0.00011
0.00010
0.00010
0.00010
0.00009
0.00009
0.00008
0.00008
0.00008
0.00008
-3.60
0.00016
0.00015
0.00015
0.00014
0.00014
0.00013
0.00013
0.00012
0.00012
0.00011
-3.50
0.00023
0.00022
0.00022
0.00021
0.00020
0.00019
0.00019
0.00018
0.00017
0.00017
-3.40
0.00034
0.00032
0.00031
0.00030
0.00029
0.00028
0.00027
0.00026
0.00025
0.00024
-3.30
0.00048
0.00047
0.00045
0.00043
0.00042
0.00040
0.00039
0.00038
0.00036
0.00035
3.20
0.00069
0.00066
0.00064
0.00062
0.00060
0.00058
0.00056
0.00054
0.00052
0.00050
-3.10
0.00097
0.00094
0.00090
0.00087
0.00084
0.00082
0.00079
0.00076
0.00074
0.00071
-3.00
0.00135
0.00131
0.00126
0.00122
0.00118
0.00114
0.00111
0.00107
0.00104
0.00100
0.00169
0.00233
-2.90
0.00187
0.00181
0.00175
0.00164
0.00159
0.00154
0.00149
0.00144
0.00139
-2.80
0.00256
0.00248
0.00240
0.00226
0.00219
0.00212
0.00205
0.00199
0.00193
-2.70
0.00347
0.00336
0.00326
0.00317
0.00307
0.00298
0.00289
0.00280
0.00272
0.00264
-2.60
0.00466
0.00453
0.00440
0.00427
0.00415
0.00402
0.00391
0.00379
0.00368
0.00357
-2.50
0.00621
0.00604
0.00587
0.00570
0.00554
0.00539
0.00523
0.00508
0.00494
0.00480
-2.40
0.00820
0.00798
0.00776
0.00755
0.00734
0.00714
0.00695
0.00676
0.00657
0.00639
-2.30
0.01072
0.01044
0.01017
0.00990
0.00964
0.00939
0.00914
0.00889
0.00866
0.00842
-2.20
0.01390
0.01355
0.01321
0.01287
0.01255
0.01222
0.01191
0.01160
0.01130
0.01101
-2.10
0.01786
0.01743
0.01700
0.01659
0.01618
0.01578
0.01539
0.01500
0.01463
0.01426
-2.00
0.02275
0.02222
0.02169
0.02118
0.02068
0.02018
0.01970
0.01923
0.01876
0.01831
-1.90
0.02872
0.02807
0.02743
0.02680
0.02619
0.02559
0.02500
0.02442
0.02385
0.02330
-1.80
0.03593
0.03515
0.03438
0.03362
0.03288
0.03216
0.03144
0.03074
0.03005
0.02938
-1.70
0.04457
0.04363
0.04272
0.04182
0.04093
0.04006
0.03920
0.03836
0.03754
0.03673
-1.60
0.05480
0.05370
0.05262
0.05155
0.05050
0.04947
0.04846
0.04746
0.04648
0.04551
-1.50
0.06681
0.06552
0.06426
0.06301
0.06178
0.06057
0.05938
0.05821
0.05705
0.05592
-1.40
0.08076
0.07927
0.07780
0.07636
0.07493
0.07353
0.07215
0.07078
0.06944
0.06811
1.30
0.09680
0.09510
0.09342
0.09176
0.09012
0.08851
0.08691
0.08534
0.08379
0.08226
-1.20
0.11507
0.11314
0.11123
0.10935
0.10749
0.10565
0.10383
0.10204
0.10027
0.09853
-1.10
0.13567
0.13350
0.13136
0.12924
0.12714
0.12507
0.12302
0.12100
0.11900
0.11702
-1.00
0.15866
0.15625
0.15386
0.15151
0.14917
0.14686
0.14457
0.14231
0.14007
0.13786
-0.90
0.18406
0.18141
0.17879
0.17619
0.17361
0.17106
0.16853
0.16602
0.16354
0.16109
-0.80
0.21186
0.20897
0.20611
0.20327
0.20045
0.19766
0.19489
0.19215
0.18943
0.18673
-0.70
0.24196
0.23885
0.23576
0.23270
0.22965
0.22663
0.22363
0.22065
0.21770
0.21476
-0.60
0.27425
0.27093
0.26763
0.26435
0.26109
0.25785
0.25463
0.25143
0.24825
0.24510
-0.50
0.30854
0.30503
0.30153
0.29806
0.29460
0.29116
0.28774
0.28434
0.28096
0.27760
-0.40
0.34458
0.34090
0.33724
0.33360
0.32997
0.32636
0.32276
0.31918
0.31561
0.31207
-0.30
0.38209
0.37828
0.37448
0.37070
0.36693
0.36317
0.35942
0.35569
0.35197
0.34827
-0.20
0.42074
0.41683
0.41294
0.40905
0.40517
0.40129
0.39743
0.39358
0.38974
0.38591
-0.10
0.46017
0.45620
0.45224
0.44828
0.44433
0.44038
0.43644
0.43251
0.42858
0.42465
0.00 (negative)
0.00 (positive)
0.50000
0.49601
0.49202
0.48803
0.48405
0.48006
0.47608
0.47210
0.46812
0.46414
0.51197
0.55172
0.50000
0.50399
0.50798
0.51595
0.51994
0.52392
0.52790
0.53188
0.53586
0.10
0.53983
0.54380
0.54776
0.55567
0.55962
0.56356
0.56749
0.57142
0.57535
0.57926
0.61791
0.20
0.58317
0.58706
0.59095
0.59483
0.59871
0.60257
0.60642
0.61026
0.61409
0.30
0.62172
0.62552
0.62930
0.63307
0.63683
0.64058
0.64431
0.64803
0.65173
0.40
0.65542
0.65910
0.66276
0.66640
0.67003
0.67364
0.67724
0.68082
0.68439
0.68793
0.50
0.69146
0.69497
0.69847
0.70194
0.70540
0.70884
0.71226
0.71566
0.71904
0.72240
0.60
0.72575
0.72907
0.73237
0.73565
0.73891
0.74215
0.74537
0.74857
0.75175
0.75490
0.70
0.75804
0.76115
0.76424
0.76730
0.77035
0.77337
0.77637
0.77935
0.78230
0.78524
0.80
0.78814
0.79103
0.79389
0.79673
0.79955
0.80234
0.80511
0.80785
0.81057
0.81327
0.90
0.81594
0.81859
0.82121
0.82381
0.82639
0.82894
0.83147
0.83398
0.83646
0.83891
1.00
0.84134
0.84375
0.84614
0.84849
0.85083
0.85314
0.85543
0.85769
0.85993
0.86214
1.10
0.86433
0.86650
0.86864
0.87076
0.87286
0.87493
0.87698
0.87900
0.88100
0.88298
1.20
0.88493
0.88686
0.88877
0.89065
0.89251
0.89435
0.89617
0.89796
0.89973
0.90147
1.30
0.90320
0.90490
0.90658
0.90824
0.90988
0.91149
0.91309
0.91466
0.91621
0.91774
1.40
0.91924
0.92073
0.92220
0.92364
0.92507
0.92647
0.92785
0.92922
0.93056
0.93189
1.50
0.93319
0.93448
0.93574
0.93699
0.93822
0.93943
0.94062
0.94179
0.94295
0.94408
1.60
0.94520
0.94630
0.94738
0.94845
0.94950
0.95053
0.95154
0.95254
0.95352
0.95449
1.70
0.95543
0.95637
0.95728
0.95818
0.95907
0.95994
0.96080
0.96164
0.96246
0.96327
1.80
0.96407
0.96485
0.96562
0.96638
0.96712
0.96784
0.96856
0.96926
0.96995
0.97062
1.90
0.97128
0.97193
0.97257
0.97320
0.97381
0.97441
0.97500
0.97558
0.97615
0.97670
2.00
0.97725
0.97778
0.97831
0.97882
0.97932
0.97982
0.98030
0.98077
0.98124
0.98169
2.10
0.98214
0.98257
0.98300
0.98341
0.98382
0.98422
0.98461
0.98500
0.98537
0.98574
2.20
0.98610
0.98645
0.98679
0.98713
0.98745
0.98778
0.98809
0.98840
0.98870
0.98899
2.30
0.98928
0.98956
0.98983
0.99010
0.99036
0.99061
0.99086
0.99111
0.99134
0.99158
2.40
0.99180
0.99202
0.99224
0.99245
0.99266
0.99286
0.99305
0.99324
0.99343
0.99361
2.50
0.99379
0.99396
0.99413
0.99430
0.99446
0.99461
0.99477
0.99492
0.99506
0.99520
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