A study is being performed to see if there is a correlation between the concentration of chromium in the blood and a suspected disease. Blood samples from a series of volunteers with a history of the disease and other indicators of susceptibility are analyzed and compared with the results from the analysis of samples from healthy control subjects. From the following results, determine whether the difference between the two groups can be ascribed to chance or whether they are real (i.e. Do the two groups have statistically different results at the 95% confidence limit?). [Hint: You must decide if the standard deviations of the two methods are statistically the same first.]
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
A study is being performed to see if there is a
concentration of chromium in the blood and a suspected disease. Blood
samples from a series of volunteers with a history of the disease and other
indicators of susceptibility are analyzed and compared with the results from
the analysis of samples from healthy control subjects. From the following
results, determine whether the difference between the two groups can be
ascribed to chance or whether they are real (i.e. Do the two groups have
statistically different results at the 95% confidence limit?). [Hint: You must
decide if the standard deviations of the two methods are statistically the
same first.]
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