(d) What happens to the interval as the level of confidence is changed? Explain why this is a logical result. As the level of confidence increases, the width of the interval decreases. This makes sense since the
(d) What happens to the interval as the level of confidence is changed? Explain why this is a logical result. As the level of confidence increases, the width of the interval decreases. This makes sense since the
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Part D
Transcribed Image Text:Question Help
The following data represent the pH of rain for a random sample of 12 rain dates. A normal
probability plot suggests the data could come from a population that is normally distributed. A
boxplot indicates there are no outliers. Complete parts a) through d) below.
5.20
5.72
4.38
4.80
5.02
4.58
4.74
5.19
4.61
4.76
4.56
5.71
Click the icon to view the table of critical t-values.
(a) Determine a point estimate for the population mean.
A point estimate for the population mean is 4.94
(Round to two decimal places as needed.)
(b) Construct and interpret a 95% confidence interval for the mean pH of rainwater. Select the correct choice below and fill in the answer boxes to complete your
choice.
(Use ascending order. Round to two decimal places as needed.)
O A. There is a 95% probability that the true mean pH of rain water is between 4.68 and 5.24
O B. There is 95% confidence that the population mean pH of rain water is between
and
C. If repeated samples are taken, 95% of them will have a sample pH of rain water between
and
(c) Construct and interpret a 99% confidence interval for the mean pH of rainwater. Select the correct choice below and fill in the answer boxes to complete your
choice.
(Use ascending order. Round to two decimal places as needed.)
O A. There is a 99% probability that the true mean pH of rain water is between 4.59 and 5.28
O B. If repeated samples are taken, 99% of them will have a sample pH of rain water between
and
O C. There is 99% confidence that the population mean pH of rain water is between
and
(d) What happens to the interval as the level of confidence is changed? Explain why this is a logical result.
As the level of confidence increases, the width of the interval decreases. This makes sense since the
Transcribed Image Text:is 99% confidence that the population mean pH of rain water is between and.
bens to
Table of Critical t-Values
i confic
- Area in
right tail
-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
1.963
1.386
0.765 0.978 1.250
31.821 63.657
6.965
318.300 636.619
31.599
12.924
1.376
3.078
6.314
2.920
12.706
4.303
15.804
127.32 1
9925 14.080 22.327
7453 10.215
Z173
5,893
1.000
0816 1.061
1886
1.638
1.533
1.476
4.849
2.353
3.182
3.482
4.541
3.747
3.365
5.841
4.604
4.032
0.941 1.190
8,610
6,869
2.132
0.741
0.727
2.776
2.571
2.999
2.757
4.773
0.920 1.156
2.015
0718
n 06 1.13A
1440
5208
5 950
1.943
1.895
2.612
3.143
3.707 4317
0,806 1.119
1415
4.785
3.833 4.501
3.690
0.711
2.517
2.998
2.449 2.896
2.398 2.821
2.359 2.764
3.499
3.355
3.250
3.169
4.029
0.706 0,889 1.106
0.703
0 700
1.397 1.860
1.833
1.812
5.408
5,041
4.781
0,883 1.100
0.879 1.093
1.383
4.297
1372
3.581
4.144
4.587
0.697
0 695
0.876
1363
1.796
2.328
2718
2.303 2,681
2,282 2.650
2.264
4.025
3.428 3.930
3.372 3852
3.326
1.088
3.497
4.437
0873 1.083
1356
1.782
2.179
2.160
2.145
2.131
4318
0870 107o
1.350
1.771
4.221
0,694
0.692
0.691
0.868
1.076
1.345
2.624
3.787
4.140
1.761
1.753
0.866
1.074
1.341
2.249
2.602
3.286
3.733
4.073
0865
1071
1337
1.746
2 583
2.120
2.110
2.101
2.093
2.086
2,235
2.224
2.214
2,205
2.197
3252 3686s
4015
1333
1320
0863
1060
1.740
2.567
2.552
3.222
3.646
3.965
3.922
3,883
3,850
0.689
0.688
0.862
0,861
1067
1.734
3.197
3.610
3.174 3.579
3.153
1328
2530
0.68
0.68
2.861
2845
1.066
1.729
1.725
0.860
1.064
132
2.528
3.552
1063
1223
1.721
1.717
1.714
1.711
1.208
2.189
2.183
2.518
2.508
0686
0.850
2831
3.527
2.080
2.074
3.135
3.119 3.505
3.104 3485
3.091
3819
0 686
2819
3 702
0,858
0858
1.061
1.060
1.059
1.058
1321
3.768
3.745
3.725
0,685
1.319
1.318
1316
2.807
2.797
2.787
2.069
2.177
0.685
0,857
0,856
3,467
0.68
2060
3.078
3.450
1319
1. 206
3067
068
0856
1058
2.056
2.162
2779
3435
3707
0.855
0,855
0.854
1057
1314
1.703
2.771
2763
2756
2.750
3.057
3.047
3421
3.408
3.690
3,674
3.650
0.684
0,68
1.056
1313
1.701
2.048
2.154
0.683
1055
1.311
1310
1.699
2.045
2.042
3.038
3.306
2.150
2.147
0.68
0,854
1.055
1,697
3.030
3.385
3.646
1.054
2.040
2.037
2.035
2.032
2.030
2.144
2.141
2.138
2.136
2.133
0.68
3633
0,853
0,853
0853
0,852
0.852
1300
1.696
2744
3.022
2738
2733
3.375
3.365
3.356
0.68
0.682
0 68
0.682
1.054
1.053
1.052
1.052
1.309
1.308
1.694
1.692
3.015
3.008
3.002
2.996
3622
3611
t your
1307
1.691
3348
3601
1.306
1.690
2.724
3.340
3 501
0.681
0852
1052
1306
2.028
3 582
2.131
2.129
2.719
2.715
1.688
2.900
3323
1.051
3.574
0,851
0851
0851 1.05o
1.30
1.687
2.985
3.326
0.68
0 68
5024
2023
2021
5 076 131a
2.971 3307
2 937
1304 16
5125
2123
1 558
0,681
0,851
1.050
1.303 1.684
2.704
3.551
120
1299
167
2000
2.678
1261
1904
2.660
5 800 2
5 887 3 19S
2.878 3.183
1043
0,67
0.846
1.042
1291
1.662
1.987
2.084
2.368
2.632
3.402
2.081
2.364
100
0.677
0.845
1.042
1290
1.660
2624
2.626
2.871
3.174
3.390
1984
1960
1282
2.613
3.291
Degrees of 0.25
Freedom
0.20
0.15
0.10 0.05
0.025
0.02
0.01
0.005 0.0025 0.001 0,0005
t-Distribution
Area in Right Tail
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