A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following confidence interval: (0.438, 0.642). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within 2% using 95% reliability.
A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following confidence interval: (0.438, 0.642). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within 2% using 95% reliability.
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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Topic Video
Question
![A confidence interval was used to estimate the proportion of statistics students that are
female. A random sample of 72 statistics students generated the following confidence interval:
(0.438, 0.642). Using the information above, what size sample would be necessary if we wanted
to estimate the true proportion to within 2% using 95% reliability.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7c797dc-7b9b-4a03-8262-7a13e1d0de65%2Fef59036e-d0ed-418f-a4c7-52533bc93b2e%2Fo7bmxu_processed.png&w=3840&q=75)
Transcribed Image Text:A confidence interval was used to estimate the proportion of statistics students that are
female. A random sample of 72 statistics students generated the following confidence interval:
(0.438, 0.642). Using the information above, what size sample would be necessary if we wanted
to estimate the true proportion to within 2% using 95% reliability.
![Table II
Normal Curve Areas
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.0
.0000
.0040
.0080
.0120
.0160
.0199
.0239
.0279
.0319
.0359
.0478
.0871
.0596
.0987
.0438
.0517
.0910
.1293
.0675
.1064
.0714
.1103
.1480
.1
.0398
.0557
.0636
.0753
.2
.0793
.0832
.0948
.1026
.1141
.3
.1179
.1217
.1255
.1331
.1368
.1406
.1443
.1517
.1844
.2190
.4
.1554
.1591
.1628
.1664
.1700
.1736
.1772
.1808
.1879
.5
.1915
.1950
.1985
.2019
.2054
.2088
.2123
.2157
.2224
.6
.2257
.2291
.2324
.2357
.2389
.2422
.2454
.2486
.2517
.2549
.2794
.3078
.2580
.2673
.2967
.7
.2611
.2642
.2704
.2734
.2764
.2823
.2852
.3051
.3315
.8
.2881
.2910
.2939
.2995
3023
.3106
.3133
.3340
.3577
.3264
3289
.3365
.3599
.9
.3159
.3186
.3212
.3238
.3389
1.0
.3413
.3438
.3461
.3485
.3508
.3531
.3554
.3621
1.1
.3643
.3665
.3686
.3708
.3729
.3749
.3770
.3790
.3810
.3830
.3849
.4032
.4192
1.2
.3869
.3888
.3907
3925
.3944
.3962
.3980
.3997
.4015
4162
.4306
1.3
.4049
.4066
.4082
.4099
.4115
.4131
.4147
.4177
.4222
.4357
1.4
.4207
.4236
.4251
.4265
.4279
.4292
.4319
1.5
4332
.4345
.4370
.4382
.4394
.4406
4418
4429
.4441
1.6
.4452
.4463
.4474
.4484
.4495
.4505
.4515
4525
4535
.4545
1.7
.4554
.4564
.4573
.4582
.4591
.4599
.4608
.4616
.4625
.4633
.4678
.4744
1.8
.4641
.4671
.4738
.4649
.4656
.4664
.4686
.4693
.4699
.4706
1.9
.4713
.4719
.4726
.4732
.4750
.4756
4761
.4767
2.0
.4772
.4778
.4783
.4788
.4793
4798
.4803
.4808
.4812
.4817
2.1
.4821
.4826
.4830
.4834
.4838
.4842
.4846
.4850
.4854
.4857
.4864
.4896
2.2
.4861
.4868
4871
.4875
.4878
.4881
.4884
.4887
.4890
.4904
.4927
2.3
.4893
.4898
.4901
.4906
.4909
.4911
.4913
.4916
.4925
.4943
.4932
.4949
2.4
.4918
.4920
.4922
4929
.4931
.4934
.4936
2.5
.4938
.4940
.4941
.4945
.4946
.4948
.4951
.4952](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7c797dc-7b9b-4a03-8262-7a13e1d0de65%2Fef59036e-d0ed-418f-a4c7-52533bc93b2e%2Ff6fnyrh_processed.png&w=3840&q=75)
Transcribed Image Text:Table II
Normal Curve Areas
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.0
.0000
.0040
.0080
.0120
.0160
.0199
.0239
.0279
.0319
.0359
.0478
.0871
.0596
.0987
.0438
.0517
.0910
.1293
.0675
.1064
.0714
.1103
.1480
.1
.0398
.0557
.0636
.0753
.2
.0793
.0832
.0948
.1026
.1141
.3
.1179
.1217
.1255
.1331
.1368
.1406
.1443
.1517
.1844
.2190
.4
.1554
.1591
.1628
.1664
.1700
.1736
.1772
.1808
.1879
.5
.1915
.1950
.1985
.2019
.2054
.2088
.2123
.2157
.2224
.6
.2257
.2291
.2324
.2357
.2389
.2422
.2454
.2486
.2517
.2549
.2794
.3078
.2580
.2673
.2967
.7
.2611
.2642
.2704
.2734
.2764
.2823
.2852
.3051
.3315
.8
.2881
.2910
.2939
.2995
3023
.3106
.3133
.3340
.3577
.3264
3289
.3365
.3599
.9
.3159
.3186
.3212
.3238
.3389
1.0
.3413
.3438
.3461
.3485
.3508
.3531
.3554
.3621
1.1
.3643
.3665
.3686
.3708
.3729
.3749
.3770
.3790
.3810
.3830
.3849
.4032
.4192
1.2
.3869
.3888
.3907
3925
.3944
.3962
.3980
.3997
.4015
4162
.4306
1.3
.4049
.4066
.4082
.4099
.4115
.4131
.4147
.4177
.4222
.4357
1.4
.4207
.4236
.4251
.4265
.4279
.4292
.4319
1.5
4332
.4345
.4370
.4382
.4394
.4406
4418
4429
.4441
1.6
.4452
.4463
.4474
.4484
.4495
.4505
.4515
4525
4535
.4545
1.7
.4554
.4564
.4573
.4582
.4591
.4599
.4608
.4616
.4625
.4633
.4678
.4744
1.8
.4641
.4671
.4738
.4649
.4656
.4664
.4686
.4693
.4699
.4706
1.9
.4713
.4719
.4726
.4732
.4750
.4756
4761
.4767
2.0
.4772
.4778
.4783
.4788
.4793
4798
.4803
.4808
.4812
.4817
2.1
.4821
.4826
.4830
.4834
.4838
.4842
.4846
.4850
.4854
.4857
.4864
.4896
2.2
.4861
.4868
4871
.4875
.4878
.4881
.4884
.4887
.4890
.4904
.4927
2.3
.4893
.4898
.4901
.4906
.4909
.4911
.4913
.4916
.4925
.4943
.4932
.4949
2.4
.4918
.4920
.4922
4929
.4931
.4934
.4936
2.5
.4938
.4940
.4941
.4945
.4946
.4948
.4951
.4952
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