(Questions 15-19] A biologist assumes that there is a linear relationship between the amount of fertilizer supplied to a tomato plant and the subsequent yield of tomatoes obtained. Eight tomato plants of the same variety were selected at random and treated weekly with a solution in which r grams of fertilizer was dissolved in a fixed quantity of water and the yield, y kilograms, of tomatoes was recorded. Plant 1 2|3 4| 5 6 7 | 8 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 3.9 4.4 5.8 6.6 | 7.0 7.1 | 7.3 7.7 [x = 22 r = 71 Ey = 49.8 Cy² = 323.76 zy = 148.3 %3D The ANOVA table for these data is given below. Source Regression Residual Total F p- value 0.0004 df MS 12.2688 1.4862 0.2477 13.755 15. Which is the correct least squares regression model for these data? (a) ŷ = 3.2524 + 1.0810r. (b) = 3.2524r + 1.0810. (c) y = 3.2524 + 1.0810r + e. (d) y = 3.2524 + 1.0810 + e. page 6 of 21 Page Total: Version 40 STA 181/1P1: September 2021 page 7 of 21 16. What is the numerical value of the observed value of the test statistic for testing for the significance of the true correlation coefficient? (a) 9.8106. (b) 7.0356. (c) 0.8919. (d) 0.9444. 17. What is the numerical value of Foba? (a) 0.2477. (b) 12.2688. (с) 49.6312. (d) 3.0390.
(Questions 15-19] A biologist assumes that there is a linear relationship between the amount of fertilizer supplied to a tomato plant and the subsequent yield of tomatoes obtained. Eight tomato plants of the same variety were selected at random and treated weekly with a solution in which r grams of fertilizer was dissolved in a fixed quantity of water and the yield, y kilograms, of tomatoes was recorded. Plant 1 2|3 4| 5 6 7 | 8 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 3.9 4.4 5.8 6.6 | 7.0 7.1 | 7.3 7.7 [x = 22 r = 71 Ey = 49.8 Cy² = 323.76 zy = 148.3 %3D The ANOVA table for these data is given below. Source Regression Residual Total F p- value 0.0004 df MS 12.2688 1.4862 0.2477 13.755 15. Which is the correct least squares regression model for these data? (a) ŷ = 3.2524 + 1.0810r. (b) = 3.2524r + 1.0810. (c) y = 3.2524 + 1.0810r + e. (d) y = 3.2524 + 1.0810 + e. page 6 of 21 Page Total: Version 40 STA 181/1P1: September 2021 page 7 of 21 16. What is the numerical value of the observed value of the test statistic for testing for the significance of the true correlation coefficient? (a) 9.8106. (b) 7.0356. (c) 0.8919. (d) 0.9444. 17. What is the numerical value of Foba? (a) 0.2477. (b) 12.2688. (с) 49.6312. (d) 3.0390.
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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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Question
![[Questions 15-19] A biologist assumes that there is a linear relationship between the amount of fertilizer supplied to a tomato
plant and the subsequent yield of tomatoes obtained. Eight tomato plants of the same variety were selected at random and
treated weekly with a solution in which r grams of fertilizer was dissolved in a fixed quantity of water and the yield, y
kilograms, of tomatoes was recorded.
2 | 3 | 4 | 5 | 6 | 7 | 8
2.0 2.5 3.0 3.5
Plant 1
1.0
1.5
4.5
3.9
4.4 5.8 6.6
7.0 | 7.1 |
7.3 7.7
Σε 22 Σ* =1 Συ = 49.8 Συ' = 32376 Σsy 145.3
The ANOVA table for these data is given below.
p- value
0.0004
Source
df
MS
Regression
12.2688
Residual
1.4862
0.2477
Total
13.755
15. Which is the correct least squares regression model for these data?
(a) ŷ = 3.2524 + 1.0810r.
(b) ỹ = 3.2524r + 1.0810.
(c) y = 3.2524 + 1.0810r + e.
(d) y = 3.2524r + 1.0810 + e.
page 6 of 21
Page Total:
Version 40
STA 181/1P1: September 2021
page 7 of 21
16. What is the numerical value of the observed value of the test statistic for testing for the significance of the true
correlation coefficient?
(a) 9.8106.
(b) 7.0356.
(c) 0.8919.
(d) 0.9444.
17. What is the numerical value of Fob.?
(a) 0.2477.
(b) 12.2688.
(c) 49.5312.
(d) 3.0390.
18. What is the numerical value of se (b)?
(a) 1.4862.
(b) 0.0236.
(c) 0.2477.
(d) 0.1536.
.
19. If the biologist also assumes that, in addition to the amount of fertilizer, the yield is also a function of atmospheric
temperature. The following table gives the results of the multiple regression analysis for these data.
Regression Summary for Dependent Variable: Yield
R = 0,94516 R = 0.89333
F(2,5) = 20.938 p- value = 0.0037
se (b,)
p- value
0.2056
t- value
|Intercept
2.7822
1.9128
1.4545
Fertilizer
1.0317
0.2557
4.0345
0.0100
Temperature0.0262
0.2546
0.1029
0.8092
Which statement is correct?
(a) The intercept is significant.
(b) Both fertilizer and temperature are significant in explaining variation is yield.
(c) The overall model is significant.
(d) The multiple regression model is î = 1.9128 + 0.2557Fertilizer + 0.1029Temperature.
20. Which one of the following is not a property of a discrete random variable?
(a) The sum of all probabilities under a discrete distribution is one.
(b) For a discrete random variable X, and for a constant integer c, P(X = c) = 0.
(c) For a discrete random variable X, and for a constant integer c, P(X > c) = P(X >c+1).
(d) For a discrete distribution, the probabilities are all between zero and one.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F555163de-6a8a-4e74-9393-f0165da49d9d%2F79648edd-0fb1-4d4f-8e0f-5c04633950fc%2Fquc6t4o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[Questions 15-19] A biologist assumes that there is a linear relationship between the amount of fertilizer supplied to a tomato
plant and the subsequent yield of tomatoes obtained. Eight tomato plants of the same variety were selected at random and
treated weekly with a solution in which r grams of fertilizer was dissolved in a fixed quantity of water and the yield, y
kilograms, of tomatoes was recorded.
2 | 3 | 4 | 5 | 6 | 7 | 8
2.0 2.5 3.0 3.5
Plant 1
1.0
1.5
4.5
3.9
4.4 5.8 6.6
7.0 | 7.1 |
7.3 7.7
Σε 22 Σ* =1 Συ = 49.8 Συ' = 32376 Σsy 145.3
The ANOVA table for these data is given below.
p- value
0.0004
Source
df
MS
Regression
12.2688
Residual
1.4862
0.2477
Total
13.755
15. Which is the correct least squares regression model for these data?
(a) ŷ = 3.2524 + 1.0810r.
(b) ỹ = 3.2524r + 1.0810.
(c) y = 3.2524 + 1.0810r + e.
(d) y = 3.2524r + 1.0810 + e.
page 6 of 21
Page Total:
Version 40
STA 181/1P1: September 2021
page 7 of 21
16. What is the numerical value of the observed value of the test statistic for testing for the significance of the true
correlation coefficient?
(a) 9.8106.
(b) 7.0356.
(c) 0.8919.
(d) 0.9444.
17. What is the numerical value of Fob.?
(a) 0.2477.
(b) 12.2688.
(c) 49.5312.
(d) 3.0390.
18. What is the numerical value of se (b)?
(a) 1.4862.
(b) 0.0236.
(c) 0.2477.
(d) 0.1536.
.
19. If the biologist also assumes that, in addition to the amount of fertilizer, the yield is also a function of atmospheric
temperature. The following table gives the results of the multiple regression analysis for these data.
Regression Summary for Dependent Variable: Yield
R = 0,94516 R = 0.89333
F(2,5) = 20.938 p- value = 0.0037
se (b,)
p- value
0.2056
t- value
|Intercept
2.7822
1.9128
1.4545
Fertilizer
1.0317
0.2557
4.0345
0.0100
Temperature0.0262
0.2546
0.1029
0.8092
Which statement is correct?
(a) The intercept is significant.
(b) Both fertilizer and temperature are significant in explaining variation is yield.
(c) The overall model is significant.
(d) The multiple regression model is î = 1.9128 + 0.2557Fertilizer + 0.1029Temperature.
20. Which one of the following is not a property of a discrete random variable?
(a) The sum of all probabilities under a discrete distribution is one.
(b) For a discrete random variable X, and for a constant integer c, P(X = c) = 0.
(c) For a discrete random variable X, and for a constant integer c, P(X > c) = P(X >c+1).
(d) For a discrete distribution, the probabilities are all between zero and one.
![[Questions 10-13] Samples of six different brands of margarine were analyzed to determine the level of physiologically active
polyunsaturated fatty acids (PAPUFA, in percentages). The following data were obtained. Use a = 0.05.
Brand
PAPUFA
A
14.1
13.6
14.4 14.3
14.10
0.36
12.8
12.5
13.4
13.0
12.3
12.80
0.43
13.5
13.4
14.1
14.3
13.83
0.44
D
13.2
12.7
12.6
13.9
13.10
0.59
17.14 0.60
17.74| 1.54
E
16.8
17.2
16.4
17.3
18.0
F
18.1
17.2
18.7
18.4
21.3
An incomplete ANOVA table for these data is given by
Analysis of Variance:
SS
PAPUFA
df
MS
F- value p- value
0.00000
Source
Between
a
43.07435
.........
.......
Within
Total
......
Boxplots of these data are shown below.
Categorized Boxplots for the different Brands
21
20
19
18
17
16
15
14
13
12
A
D
F
DMeaneSE
I MeansS0
Brand
10. Consider the ANOVA table for these data. What are the numerical values of a and b?
(a) a = 5 and b= 21
(b) a = 5 and b= 25.
(e) a = 6 and b = 27.
(d) a = 5 and b = 20.
11. Consider the ANOVA table for these data. What is the approximate numerical value of c?
(a) 140.01.
(b) 28.00.
(c) 13.68.
(d) 43.07.
page 5 of 21
Page Total:
Version 40
STA 1s1/1P1: September 2021
page 6 of 21
12. Consider the ANOVA table for these data. What conclusion can one make from this output?
(a) Ho is rejected and conclude that these data show evidence of dependence of group means.
(b) Họ is rejected and conclude that the data show evidence of group means being significantly different.
(c) Ho is not rejected and conclude that these data show evidence of independence of group means.
(d) H, is rejected and conclude that these data show evidence of group means being significantly equal.
13. Consider the boxplots of these data. Which statement is true?
(a) The group means for brands A and B are significantly different.
(b) The group means for brands B and E are not significantly different.
(c) The group means for all the brands are all significantly different.
(d) The group means for brands A and C are significantly different.
14. Suppose that X is a discrete random variable with P(X = r) given in the accompanying table.
0 |1| 2 | 3 4
P(X = x) | + | †#
Determine the mean of X.
(a) 3.1613.
(b) 1.0805.
(n) 1 1676](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F555163de-6a8a-4e74-9393-f0165da49d9d%2F79648edd-0fb1-4d4f-8e0f-5c04633950fc%2Fewu97yl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[Questions 10-13] Samples of six different brands of margarine were analyzed to determine the level of physiologically active
polyunsaturated fatty acids (PAPUFA, in percentages). The following data were obtained. Use a = 0.05.
Brand
PAPUFA
A
14.1
13.6
14.4 14.3
14.10
0.36
12.8
12.5
13.4
13.0
12.3
12.80
0.43
13.5
13.4
14.1
14.3
13.83
0.44
D
13.2
12.7
12.6
13.9
13.10
0.59
17.14 0.60
17.74| 1.54
E
16.8
17.2
16.4
17.3
18.0
F
18.1
17.2
18.7
18.4
21.3
An incomplete ANOVA table for these data is given by
Analysis of Variance:
SS
PAPUFA
df
MS
F- value p- value
0.00000
Source
Between
a
43.07435
.........
.......
Within
Total
......
Boxplots of these data are shown below.
Categorized Boxplots for the different Brands
21
20
19
18
17
16
15
14
13
12
A
D
F
DMeaneSE
I MeansS0
Brand
10. Consider the ANOVA table for these data. What are the numerical values of a and b?
(a) a = 5 and b= 21
(b) a = 5 and b= 25.
(e) a = 6 and b = 27.
(d) a = 5 and b = 20.
11. Consider the ANOVA table for these data. What is the approximate numerical value of c?
(a) 140.01.
(b) 28.00.
(c) 13.68.
(d) 43.07.
page 5 of 21
Page Total:
Version 40
STA 1s1/1P1: September 2021
page 6 of 21
12. Consider the ANOVA table for these data. What conclusion can one make from this output?
(a) Ho is rejected and conclude that these data show evidence of dependence of group means.
(b) Họ is rejected and conclude that the data show evidence of group means being significantly different.
(c) Ho is not rejected and conclude that these data show evidence of independence of group means.
(d) H, is rejected and conclude that these data show evidence of group means being significantly equal.
13. Consider the boxplots of these data. Which statement is true?
(a) The group means for brands A and B are significantly different.
(b) The group means for brands B and E are not significantly different.
(c) The group means for all the brands are all significantly different.
(d) The group means for brands A and C are significantly different.
14. Suppose that X is a discrete random variable with P(X = r) given in the accompanying table.
0 |1| 2 | 3 4
P(X = x) | + | †#
Determine the mean of X.
(a) 3.1613.
(b) 1.0805.
(n) 1 1676
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