Explanation:
Probabilities are described as ratios of favorable event outcome to the total number of event outcomes.
This is written as...
[tex]P (E) =\frac{n(E)}{n(S)} \\[/tex]
where...
E= the number of times the event occurs
S= the number of trials
In biology experiments, hypotheses are formed based on research questions, and tested with the use of variables to provide a particular outcome. Statistics allows for testing data for consistency with the hypothesis, while statistical probability testing can be used in experiments to determine a range of outcomes, from genetic inheritance, evolutionary rates to theoretical experimental results.
In these statistical models, probability distributions are functions that give probabilities for certain event outcomes within an experiment (a set of trials). These may be either continuous, taking a value within a range of two numbers; or discrete, which may be either of two specified values. Discrete probability distributions list each value that a random variable may possibly take on.
Further Explanation:
For example, two types of probability distributions are employed in experimental biology:
Binomial distributions, which are discrete distributions, provide probability of a certain number of successful events for x a random variable, in a specific number of trials, n; here, the probability of success of an individual trial is constant at P and only one of two outcomes are possible- this is sampling with replacement.
where...
b(x; n, P)-the probability that an experiment of n trials results in x successes
nCx- the number of combinations of n things at r time
[tex]b(x; n, P) = [ nCx ]* P^{x} * (1-P)^{n-x}\\[/tex]
This is often used in determining potential outcomes before data collection.
A type of continuous distribution, the student's t-test, compares standard deviations and means from two sets of samples or groups to check for significant differences between them.
[tex]t= \frac{(x_{1} - x_{2}) }{\sqrt{(\frac{(S_{1}) ^{2} }{n1} }+ (\frac{(S_{2}) ^{2} }{n2 }}[/tex]
where...
- x1 and s1 are the mean and standard deviation of sample 1 respectively
- x2 and s2 are the mean and standard deviation of sample 1 respectively
- n1 and n2 are sample sizes in samples 1 and 2 respectively
The null and alternate hypotheses typically theorize the likelihood and significance of certain event outcome probabilities. Critical values of t, along with degrees of freedom are used to determine a range of probable outcomes; probability or p- values along with this range, are used to determine whether either hypothesis is rejected or accepted.
For instance, significant differences between an experimental control and a specific treatment group would show that these occurrences are not due to sampling errors or random chance...
Learn more about calculating probability at https://brainly.com/question/4021035
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