Hypothesis testing problems
1. A study has been carried out to compare the United
Way contributions made by clerical workers from three
local corporations. A sample of clerical workers has been
randomly selected from each firm, and the dollar amounts
of their contributions are as follows. (Use data file XR12027.)
Firm 1 Firm 2 Firm 3
199 108 162
236 104 86
167 153 160
263 218 135
254 210 207
96 201
a. What are the null and alternative hypotheses for
this test?
b. Use ANOVA and the 0.05 level of significance in
testing the null hypothesis identified in part (a).
2. For the following summary table for a one-way
ANOVA, fill in the missing items (indicated by asterisks),
identify the null and alternative hypotheses, then use the
0.025 level of significance in reaching a conclusion
regarding the null hypothesis.
Variation Sum of Degrees of Mean
Source Squares Freedom Square F
Treatments 665.0 4 *** ***
Error *** 60 ***
Total 3736.3 ***
3. From the one-day work absences during the past year, the
personnel director for a large firm has identified the day of the
week for a random sample of 150 of the absences.
Given the following observed frequencies, and for
a = 0.01, can the director conclude that one-day absences
during the various days of the week are not equally likely?
Monday Tuesday Wednesday Thursday Friday
42 18 24 27 39 150
4. The outstanding balances for 500 credit-card
customers are listed in file XR13026. Using the 0.10 level of
significance, examine whether the data could have come
from a normal distribution.
Balance
3917
3968
3176
3318
4282
3666
2585
3831
3684
4213
3857
3142
2876
3925
3131
3409
3288
3221
4050
3248
2743
3613
3094
3599
3215
2818
3417
3514
3330
3623
3769
3860
3897
3514
4121
3378
3846
3401
3186
2813
3268
3762
3492
4095
4165
4252
3547
3483
3840
3691
3877
3584
3349
3541
4014
3475
2962
3618
2945
3917
2955
3119
3181
2921
4057
3379
3453
3736
3622
3338
3697
3771
3623
3512
3704
3696
3490
3722
3570
2987
3032
3813
3685
3361
3633
3472
3449
4008
3595
4263
2993
3337
2953
3742
3671
3942
3480
3576
3009
3834
3932
3383
3426
3157
3024
3444
3221
3924
3330
3391
3024
2973
3322
3472
3704
2946
3802
4397
3644
3839
3754
3503
2983
3662
3881
2836
3490
3444
3845
3544
3748
3288
3332
3497
2803
3975
2959
3318
4093
3673
3132
3516
3564
3765
3571
3848
3450
3264
4047
3503
3142
3614
3002
3110
3318
4087
3817
3719
3941
3701
3508
3262
3207
3319
4023
3451
3319
3403
3352
3416
3189
3246
3423
3742
3715
3692
3865
3878
3880
3497
3571
3465
2848
4360
3243
3402
2980
3592
3278
3875
2991
3266
3307
4191
3466
3525
3683
3601
3840
3837
3575
3702
3451
3980
4082
3472
3913
3036
3640
3202
3891
3875
3397
3716
3367
3206
3535
2926
3265
4084
3537
3382
3965
4083
3717
3048
3832
3476
3519
2870
3407
3422
3622
3281
3925
3456
3863
3776
3440
3615
3297
3452
3301
4036
3366
3827
3076
3458
3670
3388
3757
3103
4552
3804
3492
3682
3088
3099
4167
3864
3840
3569
3667
3158
3354
3351
3881
3383
2614
3244
3603
3210
2908
3560
3331
3064
3529
3352
3995
3341
3300
4334
3812
4181
3019
4163
3931
3872
3816
3730
3789
3427
2843
3204
3170
3284
3557
3427
3438
3689
4106
3036
3366
3879
3757
2993
3894
3879
4109
3536
3174
3900
3690
3157
3417
3193
3484
4389
3679
3500
3155
4167
4107
3556
3156
3821
3761
3804
3752
3638
3016
3369
2953
3547
3689
3520
3685
3253
3468
3420
3455
4155
3846
3766
3425
4182
3378
3154
3605
3735
4145
3459
3848
3137
4435
3156
3184
3738
3214
3933
3790
3677
3942
3407
3413
3391
3451
3581
3411
3409
3658
3462
3278
3783
3712
4104
3764
3920
3218
3272
3725
4054
3448
3139
3905
2862
3527
3363
3562
3593
3689
3132
3703
3922
3230
3995
3538
3451
3365
3062
3153
3618
3482
3114
3902
3763
3566
3210
3615
3264
3117
3338
3276
3353
3534
3868
3785
3700
3760
3541
3644
2903
2975
3184
3520
4044
3470
3357
3596
3094
3225
3333
3383
3877
3423
3482
3784
4086
4367
3592
3262
3755
3396
3361
3900
3459
3791
3891
3961
3184
3998
3534
3758
3375
3399
3262
4095
3544
3989
3716
3101
3458
2626
4196
3707
3766
3368
3767
3092
4269
3357
3520
3852
3137
3401
3703
3792
3458
3322
3479
2871
3777
3327
3698
3443
3927
3605
3692
3568
3733
3281
3362
3549
3684
3480
3306
3573
3187
3068
2750
5. The following data represent x = boat sales and
y = boat trailer sales from 1995 through 2000.
Boat Sales Boat Trailer Sales
Year (Thousands) (Thousands)
1995 649 207
1996 619 194
1997 596 181
1998 576 174
1999 585 168
2000 574 159
a. Determine the least-squares regression line and interpret
its slope.
b. Estimate, for a year during which 500,000 boats are
sold, the number of boat trailers that would be sold.
c. What reasons might explain why the number of boat
trailers sold per year is less than the number of
boats sold per year?
6. For each of 10 popular prescription drugs, file
XR15042 lists the retail price (in U.S. dollars) for the drug
in several different countries, including the United States,
Canada, Great Britain, and Australia. Determine and
interpret the coefficients of correlation and
determination for U.S. prices versus Canadian prices.
Drug US Price Canada Price Great Britain Price Australia Price
Prilosec 3.31 1.47 1.67 1.29
Prozac 2.27 1.07 1.08 0.82
Lipitor 2.54 1.34 1.67 1.32
Prevacid 3.13 1.34 0.82 0.83
Epogen 23.40 21.44 27.48 29.24
Zocor 3.16 1.47 1.73 1.75
Zoloft 1.98 1.07 0.95 0.84
Zyprexa 5.27 3.39 2.86 2.63
Claritin 1.96 1.11 0.41 0.48
Paxil 2.22 1.13 1.70 0.82
