Three randomly selected households are surveyed. The numbers of people in the households are 1, 3, and 8. (a) Construct a table representing the sampling distribution of the sample proportion of households with even numbers of people when samples of sizes n = 2 are randomly selected. You should follow this process: List all possible samples (with replacement!) of size 2. (Hint: There are 9 possible samples). Find the proportion of even numbers in each sample. Construct the probability distribution by listing each different sample proportion and its probability or frequency (b) Find the mean of the sampling distribution of the sample proportion of households with an even number of people. (c) Find the actual proportion of households with even numbers (from the three households sampled). (d) Based on your results, is the sample proportion an unbiased estimator of the population proportion? 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.
Three randomly selected households are surveyed. The numbers of people in the households are 1, 3, and 8.
(a) Construct a table representing the sampling distribution of the sample proportion of households with even numbers of people when samples of sizes n = 2 are randomly selected.
You should follow this process:
-
List all possible samples (with replacement!) of size 2. (Hint: There are 9 possible samples).
-
Find the proportion of even numbers in each sample.
-
Construct the
probability distribution by listing each different sample proportion and its probability orfrequency
(b) Find the mean of the sampling distribution of the sample proportion of households with an even number of people.
(c) Find the actual proportion of households with even numbers (from the three households sampled).
(d) Based on your results, is the sample proportion an unbiased estimator of the population proportion? Why orwhy not?
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