A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacteria. The table shows the results for the number of bacteria per cubic foot for both types of rooms. A normal probability plot and boxplot indicate that the data are approximately normally distributed with no outliers. Do carpeted rooms have more bacteria than uncarpeted rooms at the a = 0.05 level of significance? Full data set D Carpeted Uncarpeted 5.9 10.9 8 5.2 7.1 1.2 10.9 10.2 11.4 10 13 6.9 10.9 6.6 6.4 7.7 E Click the icon to view the Student t-distribution table. What are the null and alternative hypotheses? Ho: V versus H Calculate the test statistic, to- th = (Round to two decimal places as needed.) Now find the critical value. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) O A. ta O B. w2= Do carpeted rooms have more bacteria than uncarpeted rooms at the a = 0.05 level of significance? O A. No, because the test statistic is not in the critical region. O B. Yes, because the test statistic is in the critical region. O C. Yes, because the test statistic is not in the critical region. O D. No, because the test statistic is in the critical region.
A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacteria. The table shows the results for the number of bacteria per cubic foot for both types of rooms. A normal probability plot and boxplot indicate that the data are approximately normally distributed with no outliers. Do carpeted rooms have more bacteria than uncarpeted rooms at the a = 0.05 level of significance? Full data set D Carpeted Uncarpeted 5.9 10.9 8 5.2 7.1 1.2 10.9 10.2 11.4 10 13 6.9 10.9 6.6 6.4 7.7 E Click the icon to view the Student t-distribution table. What are the null and alternative hypotheses? Ho: V versus H Calculate the test statistic, to- th = (Round to two decimal places as needed.) Now find the critical value. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) O A. ta O B. w2= Do carpeted rooms have more bacteria than uncarpeted rooms at the a = 0.05 level of significance? O A. No, because the test statistic is not in the critical region. O B. Yes, because the test statistic is in the critical region. O C. Yes, because the test statistic is not in the critical region. O D. No, because the test statistic is in the critical region.
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section11.3: Shapes Of Distributions
Problem 8Q
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Continuous Probability Distributions
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Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
Transcribed Image Text:Area in
right tail
t-Distribution
Area in Right Tail
Degrees of
Freedom
0.25
0.20
0.15
0.10
0.05
0.025
0.02
0.01
0.005
0.0025
0.001
0.0005
1.376
1.963
1.386
1.250
1.190
1.156
6.314
2.920
2.353
2.132
2.015
12.706
4.303
3.182
31.821
6.965
4.541
3.747
3.365
63.657
9.925
5.841
4.604
1
1.000
0.816
0.765
0.741
0.727
3.078
1.886
1.638
1.533
1.476
15.894
4.849
3.482
2.999
2.757
127.321
14.089
7.453
5.598
4.773
318.309 636.619
22.327
10.215
7173
5.893
31.599
1.061
0.978
0.941
0.920
12.924
8.610
6.869
2.776
2.571
4.032
0.718
0.711
0.706
0.703
0.700
0.906
0.896
0.889
0.883
0.879
2.447
2.365
2.306
2.262
2.228
5.208
4.785
4.501
4.297
4.144
1.134
1.943
1.895
1.860
1.833
1.812
3.143
2.998
2.896
2.821
2.764
4.317
5.959
5.408
5.041
4.781
4.587
6.
7
1.440
1.415
1.119
1.108
1.100
1.093
1.397
1.383
1.372
2.612
2.517
2.449
2.398
2.359
3.707
3.499
3.355
3.250
4.029
3.833
3.690
3.581
9
10
3.169
11
12
13
14
15
0.697
0.695
0.694
0.692
0.691
0.876
0.873
0.870
0.868
0.866
1.088
1.083
1.079
1.076
1.363
1.356
1.350
1.796
1.782
1.771
1.761
1.753
2.201
2.179
2.160
2.328
2.303
2.282
2.264
2.249
2.718
2.681
2.650
2.624
2.602
3.106
3.055
3.012
2.977
2.947
3.497
3.428
3.372
3.326
3.286
4.025
3.930
3.852
3.787
3.733
4.437
4.318
4.221
4.140
4.073
1.345
1.341
2.145
1.074
2.131
2.120
2.110
2.101
2.093
2.086
4.015
3.965
1.071
1.069
1.067
1.066
1.064
1.337
1.333
1.330
1.328
1.325
1.746
1.740
1.734
1.729
1.725
2.235
16
17
18
19
20
0.690
0.689
0.688
0.688
0.687
2.583
2.567
2.552
2.539
2.528
3.252
3.222
3.197
3.174
3.153
0.865
0.863
0.862
0.861
0.860
2.224
2.214
2.205
2.921
2.898
2.878
2.861
2.845
3.686
3.646
3.610
3.579
3.552
3.922
3.883
3.850
2.197
0.686
0.686
0.685
0.685
0.684
1.063
1.061
1.060
1.059
1.058
1.323
1.321
1.319
1.318
1.316
2.080
2.074
2.069
2.064
2.060
2.518
2.508
2.500
2.492
2.485
3.135
3.119
3.104
3.091
3.078
3.527
3.505
3.485
3.467
3.450
3.819
21
22
23
24
25
0.859
0.858
0.858
0.857
0.856
1.721
1.717
1.714
1.711
1.708
2.189
2.183
2.177
2.172
2.167
2.831
2.819
2.807
2.797
2.787
3.792
3.768
3.745
3.725
26
27
28
29
0.684
0.684
0.683
0.683
0.856
0.855
0.855
0.854
0954
1.058
1.057
1.056
1.055
1.315
1.314
1.313
1.311
1.706
1.703
1.701
2.056
2.052
2.048
2.045
2.162
2.158
2.154
2.150
2.479
2.473
2.467
2.462
2.779
2.771
2.763
2.756
3.067
3.057
3.047
3.038
3.435
3.421
3.408
3.396
3 385
3.707
3.690
3.674
3.659
1.699
20
0 683
1055
1310
1607
2012
2147
2457
2750
2.030
3646
Transcribed Image Text:Full data set D
A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacteria. The table shows the results for the number of bacteria per cubic foot for both types of rooms. A normal
probability plot and boxplot indicate that the data are approximately normally distributed with no outliers. Do carpeted rooms have more bacteria than uncarpeted rooms at the a = 0.05 level of
significance?
Carpeted
11.4
10.2
Uncarpeted
10.9
10.9
5.9
10
13
6.9
10.9
8
5.2
6.6
6.4
7.7
7.1
1.2
Click the icon to view the Student t-distribution table.
What are the null and alternative hypotheses?
Ho:
versus H1:
Calculate the test statistic, to.
to = (Round to two decimal places as needed.)
%D
Now find the critical value. Select the correct choice below and fill in the answer box within your choice.
(Round to three decimal places as needed.)
O A. ta =
B. ta/2=
Do carpeted rooms have more bacteria than uncarpeted rooms at the a = 0.05 level of significance?
O A. No, because the test statistic is not in the critical region.
B. Yes, because the test statistic is in the critical region.
C. Yes, because the test statistic is not in the critical region.
D. No, because the test statistic is in the critical region.
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