Question

1 The marketing manager for the Capital Credit Union is considering developing an advertising campaign directed at female credit card customers. However, before continuing, she wants to know what the difference in average credit card balances is between male and female customers. She asked the database manager to select a random sample of 300 customers.

You may use Excel to develop necessary descriptive statistics or do them by hand. If you use Excel show your results

1. Use the sample data to construct a 95% confidence interval estimate for the difference in mean credit card balances for the difference in mean credit card balances for males and females.

(b) Interpret the interval estimate. Does there appear, from the interval, to be sufficient evidence to suggest a significant difference between male and 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

Customer

Number

Credit

Card

Account

Balance

Gender

1 =

Male 2 =

Female

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

Capital Credit Card Customers

File: Capital.xls

Column A: Customer Number

Column B: Credit Card Balance

Column C: Gender Code (1 = Male, 2 = Female)

Answer 1

The Excel output is:

S387 for А B C D E F 354 355 Hypothesis Test: Independent Groups (t-test, pooled variance) Male 758 311.95 50 Female 779.94 mean 290.51 std. dev. 50 n 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 98 df -21.94 difference (Male - Female) 90,854.25 pooled variance 301.42 pooled std. dev. 60.28 standard error of difference 0 hypothesized difference -0.364 t .7167 p-value (two-tailed) -141.57 confidence interval 95.% lower 97.69 confidence interval 95.% upper 119.63 margin of error

(a) Use the sample data to construct a 95% confidence interval estimate for the difference in mean credit card balances for the difference in mean credit card balances for males and females.

The 95% confidence interval estimate for the difference in mean credit card balances for the difference in mean credit card balances for males and females is between -141.57 and 97.69.

(b) Interpret the interval estimate. Does there appear, from the interval, to be sufficient evidence to suggest a significant difference between male and female?

We are 95% confident that the true difference in mean credit card balances for the difference in mean credit card balances for males and females is between -141.57 and 97.69.

Since the confidence interval contains 0, we cannot conclude that there is a significant difference between male and female.