Three randomly selected households are surveyed. The numbers of people in the households are 11, 33, and 88. Assume that samples of size nequals=2 are randomly selected with replacement from the population of 11, 33, and 88. Listed below are the nine different samples. Complete parts (a) through (c). a. Find the median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. b. Compare the population median to the mean of the sample medians. Choose the correct answer below. A. The population median is not equal to the mean of the sample medians (it is also not half or double the mean of the sample medians). B. The population median is equal to double the mean of the sample medians. C. The population median is equal to the mean of the sample medians. D. The population median is equal to half of the mean of the sample medians. c. Do the sample medians target the value of the population median? In general, do sample medians make good estimators of population medians? Why or why not? A. The sample medians do not target the population median, so sample medians make good estimators of population medians. B. The sample medians target the population median, so sample medians make good estimators of population medians. C. The sample medians target the population median, so sample medians do not make good estimators of population medians. D. The sample medians do not target the population median, so sample medians do not make good estimators of population medians.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Assume that samples of size nequals=2
are randomly selected with replacement from the population of
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