Based on data of people who dream in black and white or in color, people are divided into age groups. Among 306 people over the age of 55, 68 dream in black and white. Among 298 people under the age of 25, 13 dream in black and white. A 95% confidence interval is created to estimate the difference in proportion of people age over 55 that dream in black and white (group 1) and the proportion of those under 25 (group 2). The results are summarized below. Does the data suggest that the proportion of people over 55 who dream in black and white is equal to the proportion of those under 25? Why or why not?
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.
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Based on data of people who dream in black and white or in color, people are divided into age groups. Among 306 people over the age of 55, 68 dream in black and white. Among 298 people under the age of 25, 13 dream in black and white. A 95% confidence interval is created to estimate the difference in proportion of people age over 55 that dream in black and white (group 1) and the proportion of those under 25 (group 2). The results are summarized below.
Does the data suggest that the proportion of people over 55 who dream in black and white is equal to the proportion of those under 25? Why or why not?
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