1. Penicillin is produced through a fermentation process. Investigators want to
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Question
1. Penicillin is produced through a fermentation process. Investigators want to compare the yield from two different production methods. They will be testing across several days and each day they start a new fermentation. process. Under what situations might the investigators want to consider blocking on day?
2. For testing difference between the two production methods, how many numerator degrees of freedom would there be for the F-test?
3. For testing the day (block) effect, the investigators found a p-value of p=0.093. What can they conlcude?
a. There is a statistically significant association of block with production yield
b. There is no association of block and production yield
c. Unable to claim a statistically significant association between block and production yield
d. Blocking had no statistically significant association with production method.
4. If there are a sufficient number of block then the investigators could also test for an interaction term for production method and block. What would including the interaction in the model give the investigators that they would not have gotten in the previous questions?
5. What in the above design would help reduce potential bias in looking at the association of production method and yield?
Explanation / Answer
1) There are many scenarios that the investor can select the block of the day
* Water consumption for fermentation
* Catalyst ratio mixed for fermentation
The researcher tries to figure out the no. of possible experiment and they test the data collected by experiment hypothetically.
2) So degree of freedom for two variable, Let say method 1 and method 2 df is,
SSC = C - 1 where C is no. of columns
SSE = N - C where N is No. of observation
SST = N - 1
3) Before I answer this question, I must ask what is the level of significant 5% or 10% or 1%? Commonly statistician conducts the hypothesis with 5%, this varies in different cases. So, now I am assuming the level of significance as 5%. That means p-value should be less than 0.05.
H0 = There is an association between days and production yield.
H1 = There is no association between days and production yield.
Given P-value is 0.093, if the level of significance is 5% or 1% then option C will the answer. In case, Level of significance is 10%, then P-Value > than 0.1 (10%) then option A is your answer. option b and d are wrong hypothesis statement because we state at the end of hypothesis testing like "we reject the null hypothesis" or "we fail to reject the null hypothesis".
4) For instants, let's take super doper penicillin has 0.9 positive bacteria. now we are producing new drug by adding some acid to make that drug has super doper. In these kinds of situation, interaction term helps us to make the super doper drug. Following are trail and observe experiment using interaction term,
If we add, 1ml of acid then we observe penicillin has 0.2 positive bacteria,
5ml acid added we observe 0.5 positive bacteria,
10ml acid added then we observe 0.3 Positive bacteria,
6.5ml acid added we observe 0.9 positive bacteria.
From above observation, we identified optimal addition of acid is 6.5 to make the drug super doper, if we add above 6.5ml of acid we lose the drug maximum utility.
5) To make the experiment unbiased, we need to research more than our own intuition this makes the model unbiased. I mean prove all the intuition hypothetically.
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