An article in a reputable science journal presented data on the mole fraction solubility of a solute at a constant temperature. Also measured are the dispersion x, and dipolar and hydrogen bonding solubility parameters X2 and X3. A portion of the data is shown in the accompanying table. In the model, y is the negative logarithm of the mole fraction. Complete parts (a) through (c) below. Click the icon to view the mole fraction solubility data. (a) Fit the model y; = ßo + ß1×1; +ẞ2×2; + ẞ3×3; + £; for i = 1, 2, ..., 20. Test Ho: B₁ =ẞ₂ = ẞ3 = 0. ŷ= -0.269 + (0.078) ×₁ + (0.025) ×2 + ( − 0.036) ×3 (Round to three decimal places as needed.) Determine the alternative hypothesis. H₁: At least one of the coefficients is not 0. Find the test statistic. f= 35.28 (Round to two decimal places as needed.) Find the P-value. P-value= (Round to three decimal places as needed.) Mole Fraction Solubility Data Obs. y x1 x2 X3 1 0.2220 7.3 0.0 0.0 23450 2 0.3950 8.7 0.0 0.3 3 0.4220 8.8 0.7 1.0 4 0.4370 8.1 4.0 0.2 0.4280 9.0 0.5 1.0 6 0.4670 8.7 1.5 2.8 7 0.4440 9.3 2.1 1.0 8 0.3780 7.6 5.1 3.4 9 0.4940 10.0 0.0 0.3 10 0.4560 8.4 3.7 4.1 11 0.4520 9.3 3.6 2.0 12 0.1120 7.7 2.8 7.1 13 0.4320 9.8 4.2 2.0 14 0.1010 7.3 2.5 6.8 15 0.2320 8.5 2.0 6.6 16 0.3060 9.5 2.5 5.0 17 0.0923 7.4 2.8 7.8 18 0.1160 7.8 2.8 7.7 19 0.0764 7.7 3.0 8.0 20 0.4390 10.3 1.7 4.2
An article in a reputable science journal presented data on the mole fraction solubility of a solute at a constant temperature. Also measured are the dispersion x, and dipolar and hydrogen bonding solubility parameters X2 and X3. A portion of the data is shown in the accompanying table. In the model, y is the negative logarithm of the mole fraction. Complete parts (a) through (c) below. Click the icon to view the mole fraction solubility data. (a) Fit the model y; = ßo + ß1×1; +ẞ2×2; + ẞ3×3; + £; for i = 1, 2, ..., 20. Test Ho: B₁ =ẞ₂ = ẞ3 = 0. ŷ= -0.269 + (0.078) ×₁ + (0.025) ×2 + ( − 0.036) ×3 (Round to three decimal places as needed.) Determine the alternative hypothesis. H₁: At least one of the coefficients is not 0. Find the test statistic. f= 35.28 (Round to two decimal places as needed.) Find the P-value. P-value= (Round to three decimal places as needed.) Mole Fraction Solubility Data Obs. y x1 x2 X3 1 0.2220 7.3 0.0 0.0 23450 2 0.3950 8.7 0.0 0.3 3 0.4220 8.8 0.7 1.0 4 0.4370 8.1 4.0 0.2 0.4280 9.0 0.5 1.0 6 0.4670 8.7 1.5 2.8 7 0.4440 9.3 2.1 1.0 8 0.3780 7.6 5.1 3.4 9 0.4940 10.0 0.0 0.3 10 0.4560 8.4 3.7 4.1 11 0.4520 9.3 3.6 2.0 12 0.1120 7.7 2.8 7.1 13 0.4320 9.8 4.2 2.0 14 0.1010 7.3 2.5 6.8 15 0.2320 8.5 2.0 6.6 16 0.3060 9.5 2.5 5.0 17 0.0923 7.4 2.8 7.8 18 0.1160 7.8 2.8 7.7 19 0.0764 7.7 3.0 8.0 20 0.4390 10.3 1.7 4.2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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I need help with finding the p-value, please make sure to Round to three decimal places as needed for the p-value.
Transcribed Image Text:An article in a reputable science journal presented data on the mole fraction solubility of a solute at a constant
temperature. Also measured are the dispersion x, and dipolar and hydrogen bonding solubility parameters X2 and
X3. A portion of the data is shown in the accompanying table. In the model, y is the negative logarithm of the mole
fraction. Complete parts (a) through (c) below.
Click the icon to view the mole fraction solubility data.
(a) Fit the model y; = ßo + ß1×1; +ẞ2×2; + ẞ3×3; + £; for i = 1, 2, ..., 20. Test Ho: B₁ =ẞ₂ = ẞ3 = 0.
ŷ= -0.269 + (0.078) ×₁ + (0.025) ×2 + ( − 0.036) ×3
(Round to three decimal places as needed.)
Determine the alternative hypothesis.
H₁: At least one of the coefficients is not 0.
Find the test statistic.
f= 35.28
(Round to two decimal places as needed.)
Find the P-value.
P-value=
(Round to three decimal places as needed.)
Transcribed Image Text:Mole Fraction Solubility Data
Obs.
y
x1
x2
X3
1
0.2220
7.3
0.0
0.0
23450
2
0.3950
8.7
0.0
0.3
3
0.4220
8.8
0.7
1.0
4
0.4370
8.1
4.0
0.2
0.4280
9.0
0.5
1.0
6
0.4670
8.7
1.5
2.8
7
0.4440
9.3
2.1
1.0
8
0.3780
7.6
5.1
3.4
9
0.4940
10.0
0.0
0.3
10
0.4560
8.4
3.7
4.1
11
0.4520
9.3
3.6
2.0
12
0.1120
7.7
2.8
7.1
13
0.4320
9.8
4.2
2.0
14
0.1010
7.3
2.5
6.8
15
0.2320
8.5
2.0
6.6
16
0.3060 9.5
2.5
5.0
17
0.0923
7.4
2.8
7.8
18
0.1160
7.8
2.8
7.7
19
0.0764
7.7
3.0
8.0
20
0.4390
10.3
1.7
4.2
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