Using the data shown in the accompanying contingency table, test whether the population proportions differ at the a = 0.10 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the critical value. Assume that the samples are dependent and were obtained randomly. Click here to view the contingency table Click here to view the table of critical values of the chi-square distribution, (a) Let p, represent the proportion of success for treatment A and p2 represent the proportion of success for treatment B. What are the null and alternative hypotheses? O B. Ho: P1 =P2 O A. Ho: P1 P2 H,: P, =P2 H,: P, >P2 Họ: P1 =P2 H4: P, P2 OD. Ho: P1 =P2 H,: P,
Using the data shown in the accompanying contingency table, test whether the population proportions differ at the a = 0.10 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the critical value. Assume that the samples are dependent and were obtained randomly. Click here to view the contingency table Click here to view the table of critical values of the chi-square distribution, (a) Let p, represent the proportion of success for treatment A and p2 represent the proportion of success for treatment B. What are the null and alternative hypotheses? O B. Ho: P1 =P2 O A. Ho: P1 P2 H,: P, =P2 H,: P, >P2 Họ: P1 =P2 H4: P, P2 OD. Ho: P1 =P2 H,: P,
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Question
Transcribed Image Text:Using the data shown in the accompanying contingency table, test whether the population proportions differ at the a = 0.10 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the critical value.
Assume that the samples are dependent and were obtained randomly.
Click here to view the contingency table Click here to view the table of critical values of the chi-square distribution.
(a) Let p, represent the proportion of success for treatment A and p, represent the proportion of success for treatment B. What are the null and alternative hypotheses?
B. Ho: P1 = P2
A. Ho: P1 # P2
H1: P1 = P2
H1:P, > P2
C. Ho: P1 = P2
H7: P, #P2
D. Ho: P1 = P2
H1:P, <P2
(b) The test statistic is
%3D
(Round to two decimal places as needed.)
Transcribed Image Text:Chi-Square Distribution Critical Values Table
Contingency Table
Treatment A
Chi-Square (x Distribution
Areato the Right of Critical Vahue
Success
Failure
Degrees of
Success
46
30
Treatment B
Freedom
0995
0.99
0975
095
0.90
0.10
0.05
0.025
0.01
0.005
Failure
15
25
0.016
2.706
4.605
6.251
5.024
7.378
9.348
6.635
9.210
11.345
13.277
15.086
1
0.001
0.004
3.841
7879
0.061
0.216
5991
7815
10.597
0.010
0.072
0.207
2
0020
0.103
0.211
0115
0.584
1.064
1.610
3
0.352
12.838
Print
Done
14.860
16.750
0.711
7.779
11.143
0297
0554
0.484
9488
0.412
0.831
1.145
9.236
11.070
12.833
16.812
18.475
20.090
21.666
23209
0.676
0.872
1.239
1.646
2.088
2.558
1.635
2.167
2.204
2.833
3.490
4.168
4.865
10.645
12592
14.067
15.507
16.919
18.307
14.449
16.013
17535
1.237
18.548
0.989
1.690
12.017
20278
1.344
1.735
2.156
13.362
14.684
15.987
21.955
23589
25.188
2.180
2.733
2.700
3.325
19.023
10
3.247
3.940
20.483
3.816
2.603
3.074
3565
4.075
4.601
3.063
3.571
4.107
4.575
5.226
5.892
6.571
7.261
5.578
6.304
7042
17275
18.549
19.812
21.064
19.675
21.026
22.362
23.685
24.996
24.725
26 217
27688
11
21.920
26.757
12
13
4.404
5.009
5.629
6.262
23.337
24.736
26.119
28.300
29.819
4.660
5.229
14
7.790
29.141
31.319
15
8.547
22.307
27.488
30578
32.801
5142
5.697
6.265
6.844
5.812
6.408
7015
7633
8.260
26.296
27587
28.869
30.144
28.845
30.191
31.526
32.852
6.908
7564
7962
8.672
23.542
24.769
25.989
27204
34.267
35.718
37156
38.582
16
9.312
32.000
10.085
10.865
11.651
12.443
17
33.409
34.805
36.191
37566
18
8.231
9.390
8.907
9.591
19
10.117
20
7434
10.851
28.412
31.410
34.170
39.997
8.034
8.643
9.260
9.886
10.520
11.591
29.615
32.671
35.479
36.781
38.076
39.364
40.646
21
8.897
10.283
13.240
38.932
40.289
41.401
9.542
10.196
10856
11.524
22
10.982
12.338
14.041
30.813
33.924
42.796
11.689
35.172
36415
37652
41638
42.980
13.091
32.007
33.196
23
14.848
15.659
16.473
44.181
45.559
46.928
24
12.401
13.848
14.611
25
13.120
34.382
44.314
11.160
11808
12.461
38885
15.379
16.151
16.928
35.563
36.741
37.916
41.923
43.195
44.461
45.722
46.979
45.642
46.963
26
12.198
13.844
17.292
14.573
15.308
16.047
16.791
48.290
49645
50993
52.336
53672
40.113
41.337
27
12879
18.114
13.565
14.256
14.953
18.939
19.768
20.599
28
48.278
42557
29
30
13.121
13.787
49.588
50.892
17.708
39.087
40.256
18.493
43.773
51.805
63.167
55.758
67505
59.342
71.420
66.766
20.707
27991
22.164
26.509
34.764
29.051
37689
63691
76.154
24.433
40
50
29.707
32.357
79490
40 10
12100
7A 207
70 007
02 n00
00 270
01 0K
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