Hard water. In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per mil- lion, or ppm) in the drinking water. Here are the scatter- plot and regression analysis of the relationship between mortality and calcium concentration. a) Is there an association between the hardness of the water and the mortality rate? Write the appropriate hypothesis.
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.
3. Hard water. In an investigation of environmental
causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns
in England and Wales. In addition, the water hardness
was recorded as the calcium concentration (parts per mil-
lion, or ppm) in the drinking water. Here are the scatter-
plot and
mortality and calcium concentration.
a) Is there an association between the hardness of the
water and the mortality rate? Write the appropriate
hypothesis.
b) Assuming the assumptions for regression inference
are met, what do you conclude?
c) Create a 950/0 confidence interval for the slope of the
true line relating calcium concentration and mortality and Interpret your interval in context.
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