Three randomly selected households are surveyed. The numbers of people in the households are 4​, 5​, and 9. Assume that samples of size n=2 are randomly selected with replacement from the population of 4​, 5​, and 9. Listed below are the nine different samples. Complete parts​ (a) through​ (c).   4​,4    4​,5    4​,9    5​,4    5​,5    5​,9    9​,4    9​,5    9​,9    a. Find the variance of each of the nine​ samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values.   s2 Probability   ▼   0 0.3 1 ?     ▼   1 0.5 4 ?     ▼   18 4 8 ?   ▼   12.5 6.3 25 ? ​(Type an integer or a fraction. Use ascending order of the sample​ variances.)

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.