Chapter5.1

# Chapter5.1 - Chapter 5. Sampling Distribution. Introduction...

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Chapter 5. Sampling Distribution. Introduction From Chapter3, we learned the definitions of the parameter and statistic: Parameters and Statistics A parameter is a number that describes the population. A parameter is a fixed number, but in practice we do not know its value. A statistic is a number we calculate based on a sample from the population –its value can be computed once we have taken the sample, but its value varies from sample to sample. A statistic is generally used to estimate a population parameter which is a fixed but unknown number that describe the population. Why do we study Chapter 5 ? This chapter is concerned with how to learn about the value of a parameter in a population by taking a sample and studying a statistic. For example, a parameter is an attribute of the population of interest like the proportion of voters in a state that are planning to vote for

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candidate X in the next election. This proportion is unknown, but suppose we wish to learn about it. This proportion is called a parameter. We then procede by taking a sample, and calculate the proportion of voters in our sample that plan to vote for candidate X. This sample proportion is called a statistic. All statistics are computed from sample values. How does the sample statistic tell us about the population parameter? That is what this chapter is for. 5.1 Sampling Distribution for counts and Proportions The Binomial distributions for sample counts Think of tossing a coin n times as an example of the binomial setting. Each toss gives either heads or tails. The outcomes of successive tosses are independent. If we call heads a success, then p is the probability of obtaining a head. The number of heads we count is a random variable X. The distribution of X is determined by the number of observations n and the succes probability p.
Binomial Distributions The distribution of the count X of successes is called the binomial distribution with parameters n and p . The parameter n is the number of observations, and p is the probability

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## Chapter5.1 - Chapter 5. Sampling Distribution. Introduction...

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