An investigation was conducted into the dust content in the flue gases of two types of solid-fuel boilers. Thirteen boilers of type A and nine boilers of type B were used under identical fueling and extraction conditions. Over a similar period, the quantities of dust were deposited in similar traps inserted in each of the twenty-two flues. Presented below are the collected dust content (in grams) given the source broiler type. Type A 73.1 56.4 82.1 67.2 78.7 75.1 48.0 53.3 55.5 61.5 60.6 55.2 63.1 Type B 53.0 39.3 55.8 58.8 41.2 66.6 46.0 56.4 58.9 questions are in inserted image
An investigation was conducted into the dust content in the flue gases of two types of solid-fuel boilers. Thirteen boilers of type A and nine boilers of type B were used under identical fueling and extraction conditions. Over a similar period, the quantities of dust were deposited in similar traps inserted in each of the twenty-two flues. Presented below are the collected dust content (in grams) given the source broiler type. Type A 73.1 56.4 82.1 67.2 78.7 75.1 48.0 53.3 55.5 61.5 60.6 55.2 63.1 Type B 53.0 39.3 55.8 58.8 41.2 66.6 46.0 56.4 58.9 questions are in inserted image
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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Question
An investigation was conducted into the dust content in the flue gases of two types of solid-fuel boilers. Thirteen boilers of type A and nine boilers of type B were used under identical fueling and extraction conditions. Over a similar period, the quantities of dust were deposited in similar traps inserted in each of the twenty-two flues. Presented below are the collected dust content (in grams) given the source broiler type.
Type A
73.1 56.4 82.1 67.2 78.7 75.1 48.0 53.3 55.5 61.5 60.6 55.2 63.1
Type B
53.0 39.3 55.8 58.8 41.2 66.6 46.0 56.4 58.9
questions are in inserted image
Transcribed Image Text:Let difference be Type A-Type B.
answers to the following:
Provide
a. The samples are
(related/independent) samples. (1 pt)
b. At 5% alpha, perform test(s) to determine which test procedure should be
used to compare the two populations involved. For EACH test, indicate the
following: (15 pts; 1 pt each)
Ho (in words):
Ha (in words):
Test Procedure:
p-value:
Conclusion:
c. Based on the results in #1b, the appropriate test procedure to answer the
objective of the researchers is a
procedure. (1 pt)
(parametric/non-parametric) test
d. A point estimate of the average difference in dust content (g) of the two boiler
types is
(2 pts)
e. At 5% level of significance, test if the dust content (g) from Type A boilers is
greater than those from Type B boilers. (6 pts)
Ho: (in symbols)
boilers is
Ha: (in symbols).
boilers is
(in words) The average dust content from Type A
the average dust content from Type B boilers.
(in words) The average dust content from Type A
the average dust content from Type B boilers.
Test Procedure:
Justify your choice of test procedure:
p-value:
Conclusion: At alpha= 0.05,
Type A Boiler:mean = 63.83077; median = 61.5
Type B Boiler:mean = 52.88889; median = 55.8
Let difference - Type A - Type B
d=11.3
me 8.5
data Type A
W-0.94745
p-value 0.5602
Wilk-Shapiro Test for Normality
data Type B
W-0.93831
p-value 0.5643
Ha: not qual to 0
V = 74
p-value=0.00362
Ha: not equal to 0
Student's f-test on Paired Samples: Type A vs Type B
Ha: less than 0
t = 8.204
t=8.204
p-value=0.000001 p-value - 0.9998
data: difference
W 0.93134
p-value 0.3548
Wilcoxon Matched-Pairs Signed Ranks Test: Type A vs Type B
Ha: less than 0
Ha: greater than 0.
V = 74
p-value = 0.00078
V = 74
p-value 0.9999
Ha: greater than 0.
t=8.204
p-value 0.00637
F-test for Equality of Variances
F 1.3939
p-value 0.6516
Student's t-test on Two Independent Pop'n Means: Type A vs Type B
Ha: not equal to 0
t=2.5203
Ha: less than 0
t = 2.5203
p-value 0.9898
Ha: greater than 0
t = 2.5203
p-value 0.01017
p-value 0.02033
Welch's t-test on Two Independent Pop'n Means: Type A vs Type B
Ha: not equal to 0
Ha: greater than 0
t = 2.6006
Ha: less than 0
t=2.6006
p-value = 0.9912
p-value= 0.01753
t = 2.6006
p-value 0.008767
Mann-Whitney Test on Two Independent Pop'n Means: Type A vs Type B
Ha: not equal to 0
Ha: greater than 0
W - 89.5
p-value = 0.02081
W = 89.5
p-value
Ha: less than 0
W = 89.5
p-value = 0.9823
0.04162
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