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. 5.05 5.02 5.43 5.72 4.89 4.58 4.74 4,76 4.56 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 (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. If repeated samples are taken, 95% of them will have a sample pH of rain water between and O B. There is 95% confidence that the population mean pH of rain water is between and O C. There is a 95% probability that the true mean pH of rain water is 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. If repeated samples are taken, 99% of them will have a sample pH of rain water between and O B. There is a 99% probability that the true mean pH of rain water is between and O C. There is 99% confidence that the population mean pH of rain water is between and
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. 5.05 5.02 5.43 5.72 4.89 4.58 4.74 4,76 4.56 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 (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. If repeated samples are taken, 95% of them will have a sample pH of rain water between and O B. There is 95% confidence that the population mean pH of rain water is between and O C. There is a 95% probability that the true mean pH of rain water is 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. If repeated samples are taken, 99% of them will have a sample pH of rain water between and O B. There is a 99% probability that the true mean pH of rain water is between and O C. There is 99% confidence that the population mean pH of rain water is between and
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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.
5.05
5.72
4.89
4.80
5.02
4.58
4.74
5.19
5.43
4.76
4.56
5.69
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:
(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. If repeated samples are taken, 95% of them will have a sample pH of rain water between
and
O B. There is 95% confidence that the population mean pH of rain water is between
and
O C. There is a 95% probability that the true mean pH of rain water is 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. If repeated samples are taken, 99% of them will have a sample pH of rain water between
and
O B. There is a 99% probability that the true mean pH of rain water is between
and
O C. There is 99% confidence that the population mean pH of rain water is between
and
Transcribed Image Text:The following data represent the pH of rain for a random sample of 12 rain dates. A normal probability plot suggests the dat
from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts a) through d) below.
Click the icon to view the table of critical t-values.
Area in
Tight tail
(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
(Use ascending order. Round to two decimal places as needed.)
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
O A. If repeated samples are taken, 95% of them will have a sample pH of rain water between
and
15.804
4.849
3.482
2.999
2.757
1
1.000
0.816
0.765
0.741
0.727
1.376
1.061
0.978
0.941
0.920
1.963
1.386
1.250
1.190
1.156
3.078
1.886
1.638
1.533
1.476
6.314
2.920
2.353
2.132
2.015
12.706
4.303
3.182
2.776
2.571
31.821
6.965
4.541
3.747
3.365
63.657
9.925
5.841
4.604
4.032
127.32 1
14.089
7453
5.598
4.773
318.309 636.619
22.327
10.215
7173
5.893
31.599
12.924
8.610
6.869
O B. There is 95% confidence that the population mean pH of rain water is between
and
3.
4
5
O C. There is a 95% probability that the true mean pH of rain water is between
and
0.718
0.711
0.706
0.703
0.700
0.906
0.896
0.889
0,883
0.879
1.134
1.119
1.108
1.100
1.093
1.440
1.415
1.397
1.943
1.895
1.860
1.833
1.812
2.447
2.365
2.306
2.262
2.228
2.612
2.517
2.449
2.398
2.359
3.143
2.998
2.896
2.821
2.764
3.707
3.499
3.355
3.250
3.169
4.317
4.029
3.833
3.690
3.581
5.208
4.785
4.501
4.297
4.144
5.959
5.408
5.041
4.781
4.587
7
(c) Construct and interpret a 99% confidence interval for the mean pH of rainwater. Select the correct choice below and fill
(Use ascending order. Round to two decimal places as needed.)
9
10
1.383
1.372
2.328
2.303
2.282
2.264
2.249
3.497
3.428
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
1.074
1.363
1.356
1.350
1.345
1.341
1.796
1.782
1.771
1.761
1.753
2.201
2.179
2.160
2.145
2.131
2.718
2.681
2.650
2.624
2.602
3.106
3.055
3.012
2.977
2.947
4.025
3.930
3.852
3.787
3.733
4.437
4.318
4.221
4.140
4.073
O A. If repeated samples are taken, 99% of them will have a sample pH of rain water between
and
3.372
3.326
3.286
O B. There is a 99% probability that the true mean pH of rain water is between
and
16
17
18
19
20
0.690
0.689
0.688
0.688
0.687
0.865
0.863
0.862
0.861
0.860
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
2.120
2.110
2.101
2.093
2.086
2.235
2.224
2.214
2.205
2.197
2.583
2.567
2.552
2.539
2.528
2.921
2.898
2.878
2.861
2.845
3.252
3.222
3.197
3.174
3.153
3.686
3.646
3.610
3.579
3.552
O C. There is 99% confidence that the population mean pH of rain water is between
and
4.015
3.965
3.922
3.883
3.850
(d) What happens to the interval as the level of confidence is changed? Explain why this is a logical result.
21
0.686
0.859
1.063
1.323
1.721
2.080
2.189
2.518
2.831
3.135
3.527
3.819
As the level of confidence increases, the width of the interval
V This makes sense since the
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