Smokestack scrubbers Particulate matter is a serious form of air pollution often arising from industrial produc-tion. One way to reduce the pollution is to put a filter, or scrubber, at the end of the smokestack to trap the par-ticulates. An experiment to determine which smokestack scrubber design is best was run by placing four scrubbersof different designs on an industrial stack in randomorder. Each scrubber was tested 5 times. For each run, the same material was produced, and the particulate emis-sions coming out of the scrubber were measured (in parts per billion). A partially completed Analysis of Variancetable of the data follows on the next page. SourceSum ofSquaresDegrees ofFreedomMeanSquare F-Ratio Treatment 81.2Residual 30.8Total 112.0a) Calculate the mean square of the treatments and themean square of the error.b) Form the F-statistic by dividing the two mean squares.c) The P-value of this F-statistic turns out to be 0.0000949. What does this say about the null hypoth-esis of equal means? d) What assumptions have you made in order to answerpart c?e) What would you like to see in order to justify theconclusions of the F-test?f) What is the average size of the error standard deviationin particulate emissions?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
tion. One way to reduce the pollution is to put a filter,
ticulates. An experiment to determine which smokestack
of different designs on an industrial stack in random
order. Each scrubber was tested 5 times. For each run, the
sions coming out of the scrubber were measured (in parts
table of the data follows on the next page.
Sum of
Squares
Degrees of
Freedom
Mean
Square F-Ratio
Residual 30.8
Total 112.0
a) Calculate the mean square of the treatments and the
mean square of the error.
b) Form the F-statistic by dividing the two mean squares.
c) The P-value of this F-statistic turns out to be
esis of equal means?
part c?
e) What would you like to see in order to justify the
conclusions of the F-test?
f) What is the average size of the error standard deviation
in particulate emissions?
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