there are many reasons adults use credit cards. A recent survey found that 58% of adults used credit cards for convenience. a) to conduct a follow up study that would provide 95% confidence that the point estimate is correct to within+\-0.02 of the population proportion, how many people need to be sampled? b) to conduct a follow up study that would provide 95% confidence that the point assessment is correct to within +\-0.05  of the population proportion, how many people need to be sampled? c) compare the results of A and B. Below I attached pictures of the cumulative standardize normal distribution table. 
there are many reasons adults use credit cards. A recent survey found that 58% of adults used credit cards for convenience. a) to conduct a follow up study that would provide 95% confidence that the point estimate is correct to within+\-0.02 of the population proportion, how many people need to be sampled? b) to conduct a follow up study that would provide 95% confidence that the point assessment is correct to within +\-0.05  of the population proportion, how many people need to be sampled? c) compare the results of A and B. Below I attached pictures of the cumulative standardize normal distribution table. 
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
there are many reasons adults use credit cards. A recent survey found that 58% of adults used credit cards for convenience.
a) to conduct a follow up study that would provide 95% confidence that the point estimate is correct to within+\-0.02 of the population proportion, how many people need to be sampled?
b) to conduct a follow up study that would provide 95% confidence that the point assessment is correct to within
+\-0.05  of the population proportion, how many people need to be sampled?
c) compare the results of A and B.
Below I attached pictures of the cumulative standardize normal distribution table. 
Transcribed Image Text:0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.5000
0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1
0.5398
0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2
0.5793
0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.6179
0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.8186 0.8212 0.8238 G.8264 0.8289 0.8315 0.8340 0.8365 0.8389
0.3
0.4
0.6554
0.5
0.6915
0.6
0.7257
0.7
0.7580
0.8
0.7881
0.9
0.8159
1.0
0.8413
0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1
0.8643
0.8849
0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2
0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3
0.9032
0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4
0.9192
0.9332
0.9452
0.9554
0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5
1.6
0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.7
1.8
0.9641
1.9
0.9713
0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.0
0.9772
2.1
0.9821
2.2
0.9861
0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3
0.9893
0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4
0.9918
0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5
0.9938
0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6
0.9953
0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7
0.9965
0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
0.998690.998740.998780.998820.998860.998890.998930.998970.99900
0.999060.999100.999130.999160.999180.999210.999240.999260.99929
2.8
0.9974
2.9
0.9981
3.0
0.99865
3.1
0.99903
0.999340.999360.999380.999400.999420.999440.999460.999480.99950
0.999530.999550.999570.999580.999600.999610.999620.999640.99965
3.2
0.99931
3.3
3.4
0.99952
0.999680.999690.999700.999710.999720.999730.999740.999750.99976
7.999780.999780.999790.999800.999810.999810.999820.999830.99983
0.999850.999850.999860.999860.999870.999870.999880.999880.99989
0.99966
3.5
0.99977
3.6
0.99984
3.7
0.99989
0.999900.999900.999900.999910.999910.999920.999920.999920.99992
3.8
0.99993
0.999930.999930.999940.999940.999940.999940.999950.999950.99995
3.9
0.99995
0.999950.999960.999960.999960.999960.999960.999960.999970.99997
4.0
0.999968329
4.5
0.999996602
5.0
0.999999713
5.5
0.999999981
6.0
0.999999999
906
O123
Transcribed Image Text:0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
- 6.0
0.000000001
-5.5
0.000000019
- 5.0
0.000000287
-4.5
0.000003398
- 4.0
0.000031671
0.000050.0000040.000040.000040.000040.000040.000030.000030.00003
0.000070.000070.000060.000060.000060.000060.000050.000050.00005
0.000100.000100.000100.000090.000090.000080.000080.000080.00008
0.000150.000150.000140.000140.000130.000130.000120.000120.00011
0.000220.000220.000210.000200.000190.000190.000180.000170.00017
0.000320.000310.000300.000290.000280.000270.000260.000250.00024
0.000470.000450.000430.000420.000400.000390.000380.000360.00035
0.000660.000640.000620.000600.000580.000560.000540.000520.00050
0.000940.000900.000870.000840.000820.000790.000760.000740.00071
0.001310.001260.001220.001180.001140.001110.001070.001030.00100
0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
-3.9
0.00005
-3.8
0.00007
-3.7
0.00011
- 3.6
0.00016
<-3.5
0.00023
-3.4
0.00034
-3.3
-3.2
0.00048
0.00069
- 3.1
- 3.0
0.00097
0.00135
-2.9
0.0019
-2.8
0.0026
-2.7
0.0035
-2.6
0.0047
-2.5
0.0062
- 2.4
0.0082
-2.3
0.0107
-2.2
0.0139
- 2.1
- 2.0
- 1.9
- 1.8
0.0179
0.0228
0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.192 0.0188 0.0183
0.0281 0.0274 0.0268 0.0262 0.0256. 0.0250 0.0244 0.0239 0.0233
0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
0.0287
0.0359
-1.7
- 1.6
- 1.5
- 1.4
- 1.3
- 1.2
- 1.1
0.0446
0.0548
0.0668
0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
0.0808
0.0968
0.1151
0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
0.1357
-1.0
0.1587
- 0.9
- 0.8
0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
0.1841
0.2119
0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
-0.7
0.2420
0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
-0.6
0.2743
0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
0.3783 0.3745 0,3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247
0.4960 0.4920 0 4880 0 4840 0 4801 0 1761 0 1721
-0.5
0.3085
-0.4
0.3446
- 0.3
0.3821
0.4207
-0.2
- 0.1
- 0.0
0.4602
0.5000
Expert Solution
Step 1
A recent survey found that 58% of adults used credit cards for convenience.
p = 0.58
a) to conduct a follow up study that would provide 95% confidence that the point estimate is correct to within+\-0.02 of the population proportion, how many people need to be sampled?
confidence level = 0.95
Margin of error = 0.02
significance level
Critical value=
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