What is the appropriate conclusion for this test?

(Do not reject OR reject) H₀ and conclude that there (is or is not) sufficient evidence that mice with an average life span of 32 months will live to be (less or greater) than 42 months old when 40% of the calories in their diet are replaced by vitamins and protein.

Transcribed Image Text:Critical Values of the t-Distribution > > ☑= Critical Values of the t-Distribution a a 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 " 0.40 0.30 0.20 0.15 0.10 0.05 0.025 1 15.894 21.205 31.821 42.433 63.656 127.321 636.578 1 0.325 0.727 1.376 1.963 3.078 6.314 12.706 2 4.849 5.643 6.965 8.073 9.925 14.089 31.600 2 0.289 0.617 1.061 1.386 1.886 2.920 4.303 3 3.482 3.896 4.541 5.047 5.841 7.453 12.924 3 0.277 0.584 0.978 1.250 1.638 2.353 3.182 4 2.999 3.298 3.747 4.088 4.604 5.598 8.610 4 0.271 0,569 0.941 1.190 1.533 2.132 2.776 5 2.757 3.003 3.365 3.634 4.032 4.773 6.869 5 0.267 0.559 0.920 1.156 1.476 2.015 2.571 6 2.612 2.829 3.143 3.372 3.707 4.317 5.959 6 0.265 0.553 0.906 1.134 1.440 1.943 2.447 7 2.517 2.715 2.998 3.203 3.499 4.029 5.408 7 0.263 0.549 0.896 1.119 1.415 1.895 2.365 8 2.449 2.634 2.896 3.085 3.355 3.833 5.041 8 0.262 0.546 0.889 1.108 1.397 1.860 2.306 9 2.398 2.574 2.821 2.998 3.250 3.690 4.781 9 0.261 0.543 0.883 1.100 1.383 1.833 2.262 2.359 2.527 2.764 2.932 3.169 3.581 4.587 10 0.260 0.542 0.879 1.093 1.372 1.812 2.228 2.328 2.491 2.718 2.879 3.106 3.497 4.437 11 0.260 0.540 0.876 1.088 1.363 1.796 2.201 2.303 2.461 2.681 2.836 3.055 3.428 4.318 12 0.259 0.539 0.873 1.083 1.356 1.782 2.179 2.282 2.436 2.650 2.801 3.012 3.372 4.221 13 0.259 0.538 0.870 1.079 1.350 1.771 2.160 2.264 2.415 2.624 2.771 2.977 3.326 4.140 14 0.258 0.537 0.868 1.076 1.345 1.761 2.145 2.249 2.397 2.602 2.746 2.947 3.286 4.073 15 0.258 0.536 0.866 1.074 1.341 1.753 2.131 2.235 2.382 2.583 2.724 2.921 3.252 4.015 16 0.258 0.535 0.865 1.071 1.337 1.746 2.120 2.224 2.368 2.567 2.706 2.898 3.222 3.965 17 0.257 0.534 0.863 1.069 1.333 1.740 2.110 2.214 2.356 2.552 2.689 2.878 3.197 3.922 18 0.257 0.534 0.862 1.067 1.330 1.734 2.101 2.205 2.346 2.539 2.674 2.861 3.174 3.883 19 0.257 0.533 0.861 1.066 1.328 1.729 2.093 2.197 2.336 2.528 2.661 2.845 3.153 3.850 20 0.257 0.533 0.860 1.064 1.325 1.725 2.086 2.189 2.328 2.518 2.649 2.831 3.135 3.819 21 0.257 0.532 0.859 1.063 1.323 1.721 2.080 22 0.256 0.532 0.858 1.061 1.321 1.717 2.074 23 0.256 0.532 0.858 1.060 1.319 1.714 2.069 24 0.256 0.531 0.857 1.059 1.318 1.711 2.064 25 0.256 0.531 0.856 1.058 1.316 1.708 2.060 26 0.256 0.531 0.856 1.058 1.315 1.706 2.056 27 0.256 0.531 0.855 1.057 1.314 1.703 2.052 28 0.256 0.530 0.855 1.056 1.313 1.701 2.048 29 0.256 0.530 0.854 1.055 1.311 1.699 2.045 ت 30 0.256 0.530 0.854 1.055 1.310 1.697 2.042 125% 40 0.255 0.529 0.851 1.050 1.303 1.684 2.021 60 0.254 0.527 0.848 1.045 1.296 1.671 2.000 120 120 0.254 0.526 0.845 1.041 1.289 1.658 1.980 ∞ 0.253 0.524 0.842 1.036 1.282 1.645 1.960 88 888 888- 2.183 2.320 2.508 2.639 2.819 3.119 3.792 2.177 2.313 2.500 2.629 2.807 3.104 3.768 2.172 2.307 2.492 2.620 2.797 3.091 3.745 2.167 2.301 2.485 2.612 2.787 3.078 3.725 2.162 2.296 2.479 2.605 2.779 3.067 3.707 2.158 2.291 2.473 2.598 2.771 3.057 3.689 2.154 2.286 2.467 2.592 2.763 3.047 3.674 2.150 2.282 2.462 2.586 2.756 3.038 3.660 2.147 2.278 2.457 2.581 2.750 3.030 3.646 2.123 2.250 2.423 2.542 2.704 2.971 3.551 2.099 2.223 2.390 2.504 2.660 2.915 3.460 2.076 2.196 2.358 2.468 2.617 2.860 3.373 2.054 2.170 2.326 2.432 2.576 2.807 3.290 0.02 0.015 0.01 0.0075 0.005 0.0025 0.0005 " 0.40 0.30 0.20 0.15 0.10 0.05 0.025 a Q a Ο
Transcribed Image Text:A research report claims that mice with an average life span of 32 months will live to be about 42 months old when 40% of the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ<42 if 67 mice that are placed on this diet have an average life of 41 months with a standard deviation of 3.3 months? Use a P-value in your conclusion. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. Identify the null and alternative hypotheses. OA. Ho: H=42 H₁: μ#42 ○ D. Ho: #42 H₁: H=42 Find the test statistic. (Round to two decimal places as needed.) Determine the range into which the P-value falls. O B. Ho H<42 H₁:μ=42 Η μ < 42 ỌC. Ho H>42 H₁ = 42 OF Ho H=42 H₁: μ>42 this test? here sufficient evidence that mice with an average life span of 32 months will live to be than 42 months old when 40% of the calories in their diet are replaced by vitamins and protein. P-value < 0.0005 0.005 ≤ P-value <0.0075 0.0075 ≤ P-value < 0.01 0.0005 ≤ P-value < 0.0025 P-value ≥ 0.40 0.01 ≤ P-value <0.015

Question

What is the appropriate conclusion for this test?

(Do not reject OR reject) H₀ and conclude that there (is or is not) sufficient evidence that mice with an average life span of 32 months will live to be (less or greater) than 42 months old when 40% of the calories in their diet are replaced by vitamins and protein.

Critical Values of the t-Distribution
> >
☑=
Critical Values of the t-Distribution
a
a
0.02
0.015
0.01
0.0075
0.005
0.0025
0.0005
"
0.40
0.30
0.20
0.15
0.10
0.05
0.025
1
15.894
21.205
31.821
42.433
63.656
127.321
636.578
1
0.325
0.727
1.376
1.963
3.078
6.314
12.706
2
4.849
5.643
6.965
8.073
9.925
14.089
31.600
2
0.289
0.617
1.061
1.386
1.886
2.920
4.303
3
3.482
3.896
4.541
5.047
5.841
7.453
12.924
3
0.277
0.584
0.978
1.250
1.638
2.353
3.182
4
2.999
3.298
3.747
4.088
4.604
5.598
8.610
4
0.271
0,569
0.941
1.190
1.533
2.132
2.776
5
2.757
3.003
3.365
3.634
4.032
4.773
6.869
5
0.267
0.559
0.920
1.156
1.476
2.015
2.571
6
2.612
2.829
3.143
3.372
3.707
4.317
5.959
6
0.265
0.553
0.906
1.134
1.440
1.943
2.447
7
2.517
2.715
2.998
3.203
3.499
4.029
5.408
7
0.263
0.549
0.896
1.119
1.415
1.895
2.365
8
2.449
2.634
2.896
3.085
3.355
3.833
5.041
8
0.262
0.546
0.889
1.108
1.397
1.860
2.306
9
2.398
2.574
2.821
2.998
3.250
3.690
4.781
9
0.261
0.543
0.883
1.100
1.383
1.833
2.262
2.359
2.527
2.764
2.932
3.169
3.581
4.587
10
0.260
0.542
0.879
1.093
1.372
1.812
2.228
2.328
2.491
2.718
2.879
3.106
3.497
4.437
11
0.260
0.540
0.876
1.088
1.363
1.796
2.201
2.303
2.461
2.681
2.836
3.055
3.428
4.318
12
0.259
0.539
0.873
1.083
1.356
1.782
2.179
2.282
2.436
2.650
2.801
3.012
3.372
4.221
13
0.259
0.538
0.870
1.079
1.350
1.771
2.160
2.264
2.415
2.624
2.771
2.977
3.326
4.140
14
0.258
0.537
0.868
1.076
1.345
1.761
2.145
2.249
2.397
2.602
2.746
2.947
3.286
4.073
15
0.258
0.536
0.866
1.074
1.341
1.753
2.131
2.235
2.382
2.583
2.724
2.921
3.252
4.015
16
0.258
0.535
0.865
1.071
1.337
1.746
2.120
2.224
2.368
2.567
2.706
2.898
3.222
3.965
17
0.257
0.534
0.863
1.069
1.333
1.740
2.110
2.214
2.356
2.552
2.689
2.878
3.197
3.922
18
0.257
0.534
0.862
1.067
1.330
1.734
2.101
2.205
2.346
2.539
2.674
2.861
3.174
3.883
19
0.257
0.533
0.861
1.066
1.328
1.729
2.093
2.197
2.336
2.528
2.661
2.845
3.153
3.850
20
0.257
0.533
0.860
1.064
1.325
1.725
2.086
2.189
2.328
2.518
2.649
2.831
3.135
3.819
21
0.257
0.532
0.859
1.063
1.323
1.721
2.080
22
0.256
0.532
0.858
1.061
1.321
1.717
2.074
23
0.256
0.532
0.858
1.060
1.319
1.714
2.069
24
0.256
0.531
0.857
1.059
1.318
1.711
2.064
25
0.256
0.531
0.856
1.058
1.316
1.708
2.060
26
0.256
0.531
0.856
1.058
1.315
1.706
2.056
27
0.256
0.531
0.855
1.057
1.314
1.703
2.052
28
0.256
0.530
0.855
1.056
1.313
1.701
2.048
29
0.256
0.530
0.854
1.055
1.311
1.699
2.045
ت
30
0.256
0.530
0.854
1.055
1.310
1.697
2.042
125%
40
0.255
0.529
0.851
1.050
1.303
1.684
2.021
60
0.254
0.527
0.848
1.045
1.296
1.671
2.000
120
120
0.254
0.526
0.845
1.041
1.289
1.658
1.980
∞
0.253
0.524
0.842
1.036
1.282
1.645
1.960
88 888 888-
2.183
2.320
2.508
2.639
2.819
3.119
3.792
2.177
2.313
2.500
2.629
2.807
3.104
3.768
2.172
2.307
2.492
2.620
2.797
3.091
3.745
2.167
2.301
2.485
2.612
2.787
3.078
3.725
2.162
2.296
2.479
2.605
2.779
3.067
3.707
2.158
2.291
2.473
2.598
2.771
3.057
3.689
2.154
2.286
2.467
2.592
2.763
3.047
3.674
2.150
2.282
2.462
2.586
2.756
3.038
3.660
2.147
2.278
2.457
2.581
2.750
3.030
3.646
2.123
2.250
2.423
2.542
2.704
2.971
3.551
2.099
2.223
2.390
2.504
2.660
2.915
3.460
2.076
2.196
2.358
2.468
2.617
2.860
3.373
2.054
2.170
2.326
2.432
2.576
2.807
3.290
0.02
0.015
0.01
0.0075
0.005
0.0025
0.0005
"
0.40
0.30
0.20
0.15
0.10
0.05
0.025
a
Q
a
Ο

A research report claims that mice with an average life span of 32 months will live to be about 42 months old when 40% of the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ<42 if 67 mice that are placed on this diet have an
average life of 41 months with a standard deviation of 3.3 months? Use a P-value in your conclusion.
Click here to view page 1 of the table of critical values of the t-distribution.
Click here to view page 2 of the table of critical values of the t-distribution.
Identify the null and alternative hypotheses.
OA. Ho: H=42
H₁: μ#42
○ D. Ho: #42
H₁: H=42
Find the test statistic.
(Round to two decimal places as needed.)
Determine the range into which the P-value falls.
O B. Ho H<42
H₁:μ=42
Η μ < 42
ỌC. Ho H>42
H₁ = 42
OF Ho H=42
H₁: μ>42
this test?
here
sufficient evidence that mice with an average life span of 32 months will live to be
than 42 months old when 40% of the calories in their diet are replaced by vitamins and protein.
P-value < 0.0005
0.005 ≤ P-value <0.0075
0.0075 ≤ P-value < 0.01
0.0005 ≤ P-value < 0.0025
P-value ≥ 0.40
0.01 ≤ P-value <0.015

Accepted Answer

Sample size n=67Sample mean=41Sample standard deviation=3.3

of the table of critical values of the t-distribution. native hypotheses. al places as needed.) which the P-value falls. 05 .0075 0.01 0.0025 0 .015 OB. Ho: <42 H₁: 42 O E. Ho: 42 Μη με 42 this test? here sufficient evidence that mice with an average life span of 32 months will live to be