In Exercises, use the same population of {4, 5, 9} that was used in Examples 1 and 2. As in Examples 1 and 2, assume that samples of size n=2 are randomly selected with replacement. Sampling Distribution of the Sample Median a. Find the value of the population median. b. Table 6-3 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample median. Then combine values of the median that are the same, as in Table 6-4. (Hint: See Example 1 for Tables 6-3 and 6-4 that describe the sampling distribution of the sample mean.) c. Find the mean of the sampling distribution of the sample median. d. Based on the preceding results, is the sample median an unbiased estimator of the population median? Why or why not? Example 1 Sampling Distribution of the Sample Mean
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
In Exercises, use the same population of {4, 5, 9} that was used in Examples 1 and 2. As in Examples 1 and 2, assume that samples of size n=2 are randomly selected with replacement.
Sampling Distribution of the Sample
a. Find the value of the population median.
b. Table 6-3 describes the sampling distribution of the sample
c. Find the mean of the sampling distribution of the sample median.
d. Based on the preceding results, is the sample median an unbiased estimator of the population median? Why or why not?
Example 1 Sampling Distribution of the Sample Mean
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