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. 5.58 5.02 5.72 4.60 5.24 4.74 4.61 4.76 4.56 E 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. There is a 95% probability that the true mean pH of rain water is between and O B. If repeated samples are taken, 95% of them will have a sample pH of rain water between and. OC. There is 95% confidence that the population 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. There is 99% confidence that the population mean pH of rain water between and. O B. There is a 99% probability that the true mean pH of rain water is between and OC. If repeated samples are taken, 99% of them will have a sample pH of rain water 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. 5.58 5.02 5.72 4.60 5.24 4.74 4.61 4.76 4.56 E 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. There is a 95% probability that the true mean pH of rain water is between and O B. If repeated samples are taken, 95% of them will have a sample pH of rain water between and. OC. There is 95% confidence that the population 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. There is 99% confidence that the population mean pH of rain water between and. O B. There is a 99% probability that the true mean pH of rain water is between and OC. If repeated samples are taken, 99% of them will have a sample pH of rain water between and
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
Related questions
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
1.000
1.963
1.386
1.250
1.190
1.156
3.078
1.886
1.638
1.533
1.476
12.706
4.303
3.182
2.776
2.571
31.821
6.965
4.541
3.747
3.365
318.309 636.619
22.327
10.215
7173
5.893
1
0.816
0.765
0.741
0.727
1.376
1.061
0.978
0.941
0.920
6.314
2.920
2.353
2.132
2.015
15.894
4.849
3.482
2.999
2.757
63.657
9.925
5.841
4.604
4.032
127.321
14.089
7.453
5.598
4.773
31.599
12.924
8.610
6.869
3
4
3.707
3.499
3.355
3.250
3.169
5.959
5.408
5.041
1.134
0.718
0.711
0.706
0.703
0.700
0.906
0.896
0.889
0.883
0.879
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
4.317
4.029
3.833
3.690
3.581
5.208
4.785
4.501
4.297
4.144
1.383
4.781
4.587
10
1.372
0.876
0.873
0.870
0.868
1.088
1.083
1.079
1.076
4.025
3.930
1.363
2.201
11
12
13
14
15
2.718
2.681
2.650
2.624
4.437
4.318
4.221
0.694
0.692
0.691
0.697
0.695
1.356
1.350
1.345
1.796
1.782
1.771
2.179
2.160
2.145
2.131
2.328
2.303
2.282
3.106
3.055
3.012
3.497
3.428
3.372
3.326
3.286
3.852
3.787
3.733
1.761
1.753
2.264
2.249
2.977
4.140
0.866
1.074
1.341
2.602
2.947
4.073
1.337
1.333
1.330
1.328
1.325
0.865
1.071
2.235
2.224
2.214
2.205
2.197
2.583
2.567
2.552
2.539
2.528
3.252
3.222
16
17
18
19
20
3.686
3.646
3.610
3.579
3.552
4.015
3.965
3.922
3.883
3.850
0.690
0.689
0.688
0.688
0.687
1.746
1.740
1.734
1.729
1.725
2.120
2.110
2.101
2.093
2.086
2.921
2.898
2.878
2.861
2.845
0.863
0.862
1.069
1.067
1.066
1.064
3.197
3.174
3.153
0.861
0.860
0.686
0.686
0.685
0.685
0.684
1.323
1.321
1.319
1.318
1.721
1.717
1.714
1.711
1.708
2.080
2.074
2.069
2.064
2.060
2.189
2.183
2.177
2.172
2.167
3.135
3.119
3.104
21
22
0.859
0.858
0.858
1.063
1.061
1.060
1.059
1.058
2.518
2.506
2.500
2.492
2.485
2.831
2.819
2.807
2.797
2.787
3.527
3.505
3.485
3.467
3.819
3.792
3.768
3.745
3.725
3.091
3.078
0.857
25
0.856
1.316
3.450
26
27
28
29
30
0.684
0.684
0.683
0.856
0.855
0.855
0.854
0.854
1.058
1.057
1.056
1.055
1.055
1.315
1.314
1.313
1.706
1.703
1.701
1.699
1.697
2.056
2.052
2.048
2.045
2.042
2.162
2.158
2.154
2.150
2.147
2.479
2.473
2.467
2.462
2.457
2.779
2.771
2.763
2.756
2.750
3.067
3.057
3.047
3.038
3.030
3.435
3.421
3.408
3.396
3.385
3.707
3.690
3.674
3.659
3.646
0.683
1.311
1.310
0.683
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.
5.58
5.72
5.24
4.80
5.02
4.60
4.74
5.19
4.61
4.76
4.56
5.70
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. There is a 95% probability that the true mean pH of rain water is between
and
B. If repeated samples are taken, 95% of them will have a sample pH of rain water between
and
O C. There is 95% confidence that the population 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. There is 99% confidence that the population mean pH of rain water is between
and
O B. There is a 99% probability that the true mean pH of rain water is between
and
O C. If repeated samples are taken, 99% of them will have a sample pH of rain water 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
This makes sense since the
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