University of South Florida Linear Programs and The Simplex Algorithm Exercises

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I need help with my stats homework it’s only 6 questions thank you

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) Math 159 Chapter 12.2 and 12.4 classwork Name: 1) A study found that there is a correlation between numbers of TV ads subscripted and the number of cars sold in a dealership. Can we conclude that TV ads cause a change in number of cars sold in the dealership? Explain. 2) Write the possible correlation coefficient r for each of the following scatter plots from the choice of r=0.6, r= -0.8 or r= 0 r= 3) Write the correlation coefficient r for each of following scatter plots from :- 0.85, -0.4, 0.5, 0, 0.9 ,0.99 b. a. c. d. e. f. 4) Determine if there is sufficient evidence of linear correlation if a) n = 15, critical value = +/-0.514 and r= -0.633 (yes/no) b) n= 15, critical value = +/-0.514 and r=0.443 (yes / no) c) n= 15, p-value = 0.098, and a = 0.05 (yes/no) d) n= 15, p-value = 0.0098 and a = 0.01 (yes/no) 5) Given the matched pair data that records speed and noise level of 8 cars: speed(km/hr) 28 36 39 29 30 30 29 33 noise(dB) 78 79 81 79 79 79 79 80 a) Sketch a scatter plot below and describe the direction and strength of linear correlation. 4b) Compare r with the critical value to determine if there is linear correlation between speed and noise. Use a = 0.05. Round r to 3 decimal places. 1 6) Given the wheel diameter and rolling distance of skate boards below. Wheel diameter (in.) 1 2 3.5 5 5.5 7 8.5 9.5 Rolling Distance (in.) 17 23 32 30 36 52 57 55 a) Sketch a scatter plot below and describe strength of correlation and direction. 10 70 b) Find p-value from linear correlation result. Use a = 0.05 to conclude if there is sufficient evidence of linear correlation. d) Does it appear wheeling diameter of skateboard is somehow correlated to rolling distance? Х 7) Given the matched pair data below: x = score on measures of test anxiety for 9 students, where high value indicates a high level of anxiety. y = Exam scores for a sample of the same 9 students. 23 14 14 0 17 20 20 15 21 Y 43 59 48 77 50 52 46 51 51 a) Construct a scatter plot and sketch the scatter plot below. Describe the result from scatter plot. Are there any outliers? b) Find the correlation coefficient r (round to 3 decimal places) and use it to determine if linear correlation exist by comparing with the critical value. Use significant level = 0.05. c) Repeat with hypothesis test with p-value to determine if linear correlation exists. Use significant level of 0.05. Is the result consistent with the result in b? d) Based on the result above, is it reasonable to conclude that test anxiety is the cause for poor exam performance? Explain.
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Linear programs and the simplex algorithm
1.1

[25 marks total]

[7 marks]
The following figure is a graphical presentation of a linear program in standard form with slack
variables x3 , x4 , and x5 . As in the lecture, the darker area of a black solid line marks the area
where xi ≥ 0.
Your task is to list all bases that correspond to basic feasible solutions. Give a detailed reason
for your answer.
x5 = 0
x3 = 0

x4 = 0

c

x2 = 0

x1 = 0

1.2

[10 marks]
Given the following linear program in dictionary format, decide whether or not the optimal
objective function value is 17. Give a detailed reason for your answer.
max ζ
subject to x1
x4
x2

1.3

= 17 +x3 −4x5
= 1 −x3
=
−x3
+x5
= 1 +x3 −x5

[8 marks]
For some linear programs it is not obvious if they have any feasible solutions. Describe a
method that can answer whether or not a linear program has a feasible solution.

PAPER CODE COMP331

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Anonymous
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