Discussion:
Q: The Capital Bank Marketing Department has recently conducted a study of a sample of the bank's customers. At issue is whether there is a difference between the mean credit card balance between female and male customers. If they find that the two groups differ, they will target the lower group with a marketing campaign designed to increase their use of the credit card. The sample data for this study are in the file called Capital.
a) Calculate the mean and variance of the credit card balances for the male customers and the mean and variance of the credit card balances for the female customers.
b) Based on just these two calculations, would you guess that there is a significant difference between the two means? Between the two variances?
c) What conclusion should the Capital Bank reach about the mean balances for male and female customers? State the appropriate null and alternative hypotheses, and test at a significance level alpha = .05 whether they have the same means of their credit card balances.
d) Is there reason to believe that the two groups differ with respect to variability of account balance? State the appropriate null and alternative hypotheses, and test at a significance level of alpha =.02 whether they have the same the variances of their credit card balances.
| Customer Number |
Credit Card Account Balance |
Gender 1 = Male 2 = Female |
| 51130 |
$1,018.00 |
1 |
| 61413 |
$1,021.00 |
1 |
| 54713 |
$1,081.00 |
1 |
| 79247 |
$ 300.00 |
1 |
| 94899 |
$ 769.00 |
2 |
| 48035 |
$ 486.00 |
1 |
| 81473 |
$ 716.00 |
1 |
| 47715 |
$1,013.00 |
1 |
| 77905 |
$ 440.00 |
1 |
| 87443 |
$1,246.00 |
2 |
| 67666 |
$1,254.00 |
1 |
| 51470 |
$ 191.00 |
1 |
| 79898 |
$ 797.00 |
1 |
| 98615 |
$1,127.00 |
1 |
| 54278 |
$ 646.00 |
1 |
| 58800 |
$1,212.00 |
2 |
| 73680 |
$1,036.00 |
1 |
| 75732 |
$ 477.00 |
1 |
| 48393 |
$ 591.00 |
1 |
| 49325 |
$ 886.00 |
1 |
| 87544 |
$1,060.00 |
1 |
| 62798 |
$ 671.00 |
2 |
| 46295 |
$ 608.00 |
1 |
| 43091 |
$1,390.00 |
2 |
| 64924 |
$ 910.00 |
1 |
| 67327 |
$ 753.00 |
1 |
| 57645 |
$ 705.00 |
1 |
| 65922 |
$ 794.00 |
1 |
| 97105 |
$1,307.00 |
1 |
| 66453 |
$ 797.00 |
2 |
| 94755 |
$ 239.00 |
1 |
| 98308 |
$ 600.00 |
2 |
| 99475 |
$ 299.00 |
1 |
| 46744 |
$1,042.00 |
1 |
| 60688 |
$ 856.00 |
1 |
| 85470 |
$1,242.00 |
2 |
| 91810 |
$1,107.00 |
1 |
| 49362 |
$ 457.00 |
2 |
| 45455 |
$1,235.00 |
1 |
| 55927 |
$ 576.00 |
1 |
| 92473 |
$ 260.00 |
1 |
| 101250 |
$ 677.00 |
1 |
| 55339 |
$ 848.00 |
1 |
| 62698 |
$ 945.00 |
1 |
| 60050 |
$ 339.00 |
1 |
| 64580 |
$ 877.00 |
2 |
| 48057 |
$1,369.00 |
1 |
| 55042 |
$1,089.00 |
1 |
| 43374 |
$ 654.00 |
1 |
| 72733 |
$ 143.00 |
1 |
| 86396 |
$ 692.00 |
1 |
| 61283 |
$ 584.00 |
2 |
| 64707 |
$ 892.00 |
1 |
| 70424 |
$ 890.00 |
1 |
| 89647 |
$ 653.00 |
1 |
| 63628 |
$ 413.00 |
1 |
| 78783 |
$ 449.00 |
1 |
| 95629 |
$ 720.00 |
1 |
| 85903 |
$ 544.00 |
1 |
| 66676 |
$ 680.00 |
1 |
| 77736 |
$1,072.00 |
1 |
| 63228 |
$1,143.00 |
1 |
| 81121 |
$1,008.00 |
1 |
| 43483 |
$ 587.00 |
2 |
| 78777 |
$ 843.00 |
1 |
| 82188 |
$ 459.00 |
2 |
| 84472 |
$ 772.00 |
2 |
| 79090 |
$ 606.00 |
1 |
| 64652 |
$ 471.00 |
2 |
| 66220 |
$ 910.00 |
1 |
| 72295 |
$ 554.00 |
1 |
| 92462 |
$ 666.00 |
1 |
| 98392 |
$ 607.00 |
1 |
| 93792 |
$1,029.00 |
1 |
| 66697 |
$ 476.00 |
1 |
| 62626 |
$ 359.00 |
1 |
| 76586 |
$ 600.00 |
1 |
| 95690 |
$ 761.00 |
1 |
| 50516 |
$ 731.00 |
1 |
| 79313 |
$ 757.00 |
1 |
| 69664 |
$ 441.00 |
1 |
| 83704 |
$ 436.00 |
1 |
| 76457 |
$ 974.00 |
1 |
| 53428 |
$ 941.00 |
1 |
| 47003 |
$ 889.00 |
1 |
| 43834 |
$ 819.00 |
1 |
| 49761 |
$ 536.00 |
2 |
| 43392 |
$ 946.00 |
1 |
| 56517 |
$ 870.00 |
2 |
| 101786 |
$ 164.00 |
1 |
| 87478 |
$ 321.00 |
2 |
| 63356 |
$ 99.00 |
1 |
| 80646 |
$ 568.00 |
1 |
| 84154 |
$ 782.00 |
1 |
| 85553 |
$1,050.00 |
2 |
| 86982 |
$ 890.00 |
1 |
| 93119 |
$ 725.00 |
2 |
| 52389 |
$ 538.00 |
1 |
| 63190 |
$ 746.00 |
1 |
| 82127 |
$ 805.00 |
2 |
| 83665 |
$ 850.00 |
2 |
| 84782 |
$ 736.00 |
2 |
| 97458 |
$ 917.00 |
1 |
| 63147 |
$ 849.00 |
1 |
| 90412 |
$ 977.00 |
2 |
| 95964 |
$ 402.00 |
1 |
| 84773 |
$1,202.00 |
1 |
| 56713 |
$ 539.00 |
1 |
| 67695 |
$1,256.00 |
1 |
| 89606 |
$ 981.00 |
1 |
| 80900 |
$ 512.00 |
1 |
| 89033 |
$ 639.00 |
1 |
| 53115 |
$1,316.00 |
1 |
| 58606 |
$ 642.00 |
2 |
| 62666 |
$ 588.00 |
1 |
| 90377 |
$ 600.00 |
1 |
| 98048 |
$ 465.00 |
1 |
| 49660 |
$ 664.00 |
2 |
| 44797 |
$ 682.00 |
2 |
| 67122 |
$ 753.00 |
1 |
| 61982 |
$ 650.00 |
2 |
| 91135 |
$1,184.00 |
1 |
| 61494 |
$ 959.00 |
1 |
| 73726 |
$1,313.00 |
1 |
| 67693 |
$ 748.00 |
1 |
| 77065 |
$1,383.00 |
2 |
| 97948 |
$ 442.00 |
1 |
| 92509 |
$ 859.00 |
1 |
| 81874 |
$ 604.00 |
2 |
| 93793 |
$ 445.00 |
1 |
| 87317 |
$ 772.00 |
2 |
| 80635 |
$1,443.00 |
1 |
| 84671 |
$ 939.00 |
1 |
| 70391 |
$ 618.00 |
1 |
| 58305 |
$ 331.00 |
1 |
| 49880 |
$1,168.00 |
1 |
| 80319 |
$1,234.00 |
1 |
| 87552 |
$1,241.00 |
1 |
| 64206 |
$ 523.00 |
2 |
| 75028 |
$ 609.00 |
1 |
| 79482 |
$1,077.00 |
2 |
| 44330 |
$1,203.00 |
2 |
| 99760 |
$1,275.00 |
1 |
| 96522 |
$ 569.00 |
1 |
| 93072 |
$ 665.00 |
1 |
| 78036 |
$ 355.00 |
2 |
| 60716 |
$ 258.00 |
1 |
| 79617 |
$ 530.00 |
1 |
| 86455 |
$ 961.00 |
1 |
| 73125 |
$ 723.00 |
2 |
| 73650 |
$1,493.00 |
2 |
| 92708 |
$ 775.00 |
1 |
| 54901 |
$ 533.00 |
1 |
| 78485 |
$ 851.00 |
1 |
| 99847 |
$ 521.00 |
2 |
| 79580 |
$1,068.00 |
2 |
| 48061 |
$ 382.00 |
1 |
| 90133 |
$ 885.00 |
1 |
| 49516 |
$ 588.00 |
1 |
| 99834 |
$ 974.00 |
2 |
| 62034 |
$ 871.00 |
1 |
| 49395 |
$ 844.00 |
1 |
| 97765 |
$ 877.00 |
1 |
| 85280 |
$ 849.00 |
2 |
| 50826 |
$ 526.00 |
1 |
| 88733 |
$ 521.00 |
2 |
| 75843 |
$ 853.00 |
1 |
| 68292 |
$ 749.00 |
1 |
| 96944 |
$ 392.00 |
1 |
| 57798 |
$ 772.00 |
1 |
| 52402 |
$ 759.00 |
1 |
| 51085 |
$ 627.00 |
1 |
| 84209 |
$ 565.00 |
1 |
| 58209 |
$ 808.00 |
1 |
| 69544 |
$ 428.00 |
2 |
| 47839 |
$ 778.00 |
1 |
| 63596 |
$1,141.00 |
2 |
| 50305 |
$ 637.00 |
2 |
| 57900 |
$ 205.00 |
1 |
| 74405 |
$ 831.00 |
2 |
| 49336 |
$ 629.00 |
1 |
| 78629 |
$ 660.00 |
2 |
| 76518 |
$ 714.00 |
1 |
| 72358 |
$ 620.00 |
2 |
| 72619 |
$1,354.00 |
1 |
| 88105 |
$ 586.00 |
1 |
| 84285 |
$ 662.00 |
1 |
| 87317 |
$ 456.00 |
1 |
| 78263 |
$1,173.00 |
1 |
| 90124 |
$ 691.00 |
2 |
| 55106 |
$ 650.00 |
1 |
| 82469 |
$ 281.00 |
2 |
| 67636 |
$ 990.00 |
1 |
| 74573 |
$ 341.00 |
1 |
| 67625 |
$1,374.00 |
1 |
| 70749 |
$ 875.00 |
1 |
| 73196 |
$ 449.00 |
1 |
| 63504 |
$ 577.00 |
1 |
| 91214 |
$ 565.00 |
1 |
| 67756 |
$ 462.00 |
1 |
| 64985 |
$ 684.00 |
1 |
| 66002 |
$1,118.00 |
1 |
| 68363 |
$ 538.00 |
1 |
| 64181 |
$ 529.00 |
1 |
| 101477 |
$ 885.00 |
1 |
| 87592 |
$ 805.00 |
1 |
| 75756 |
$ 483.00 |
1 |
| 65109 |
$1,085.00 |
1 |
| 98110 |
$ 820.00 |
1 |
| 74941 |
$1,224.00 |
1 |
| 73702 |
$ 604.00 |
1 |
| 92035 |
$ 726.00 |
1 |
| 71132 |
$ 413.00 |
1 |
| 70326 |
$1,087.00 |
1 |
| 56077 |
$ 200.00 |
1 |
| 73772 |
$1,038.00 |
1 |
| 48358 |
$ 230.00 |
1 |
| 93150 |
$ 863.00 |
1 |
| 49906 |
$ 519.00 |
1 |
| 67375 |
$ 555.00 |
1 |
| 80399 |
$ 275.00 |
1 |
| 83558 |
$ 373.00 |
1 |
| 49713 |
$ 139.00 |
2 |
| 68827 |
$1,086.00 |
2 |
| 89168 |
$ 961.00 |
2 |
| 91836 |
$ 773.00 |
1 |
| 62766 |
$ 738.00 |
2 |
| 96938 |
$ 259.00 |
1 |
| 47844 |
$1,044.00 |
2 |
| 79321 |
$1,026.00 |
1 |
| 47465 |
$ 623.00 |
1 |
| 52546 |
$ 135.00 |
2 |
| 47347 |
$ 956.00 |
1 |
| 59758 |
$ 774.00 |
1 |
| 102699 |
$1,094.00 |
1 |
| 97051 |
$1,017.00 |
1 |
| 77050 |
$1,049.00 |
2 |
| 68010 |
$1,086.00 |
1 |
| 84631 |
$1,301.00 |
1 |
| 83033 |
$ 600.00 |
2 |
| 44171 |
$ 731.00 |
1 |
| 79188 |
$ 450.00 |
1 |
| 99198 |
$ 304.00 |
1 |
| 53245 |
$ 959.00 |
1 |
| 101862 |
$ 774.00 |
1 |
| 92131 |
$ 951.00 |
1 |
| 77483 |
$ 558.00 |
2 |
| 98384 |
$ 607.00 |
1 |
| 53542 |
$ 924.00 |
2 |
| 76241 |
$ 410.00 |
1 |
| 63996 |
$ 905.00 |
1 |
| 75381 |
$ 692.00 |
1 |
| 84477 |
$1,197.00 |
2 |
| 56138 |
$ 907.00 |
2 |
| 91392 |
$ 598.00 |
1 |
| 81639 |
$ 217.00 |
1 |
| 73573 |
$ 687.00 |
1 |
| 93747 |
$ 936.00 |
1 |
| 60067 |
$ 667.00 |
1 |
| 66591 |
$ 837.00 |
1 |
| 99917 |
$1,084.00 |
1 |
| 78809 |
$ 553.00 |
1 |
| 71275 |
$ 960.00 |
1 |
| 81841 |
$ 767.00 |
1 |
| 63391 |
$ 974.00 |
1 |
| 56713 |
$ 977.00 |
1 |
| 57038 |
$1,143.00 |
1 |
| 96465 |
$1,018.00 |
1 |
| 64600 |
$ 990.00 |
2 |
| 95910 |
$ 767.00 |
1 |
| 64293 |
$ 468.00 |
1 |
| 91212 |
$ 681.00 |
2 |
| 69280 |
$ 571.00 |
1 |
| 60337 |
$ 366.00 |
1 |
| 97075 |
$ 635.00 |
1 |
| 85126 |
$ 576.00 |
1 |
| 78298 |
$ 619.00 |
2 |
| 45968 |
$ 358.00 |
1 |
| 86616 |
$ 660.00 |
1 |
| 81367 |
$ 792.00 |
2 |
| 55469 |
$ 389.00 |
1 |
| 90050 |
$ 988.00 |
1 |
| 44269 |
$1,070.00 |
1 |
| 70409 |
$1,089.00 |
2 |
| 46674 |
$ 511.00 |
1 |
| 93897 |
$ 701.00 |
1 |
| 58338 |
$ 148.00 |
1 |
| 77379 |
$ 933.00 |
1 |
| 45422 |
$ 681.00 |
1 |
| 82331 |
$ 224.00 |
1 |
| 68594 |
$1,043.00 |
1 |
| 88824 |
$ 513.00 |
1 |
| 98974 |
$ 407.00 |
2 |
| 44355 |
$ 518.00 |
1 |
| 48887 |
$1,363.00 |
1 |
| 87971 |
$ 906.00 |
1 |
| 88935 |
$1,214.00 |
1 |
| 83976 |
$ 730.00 |
1 |
| 46938 |
$1,089.00 |
1 |
| 94387 |
$1,115.00 |
1 |