ch25inferencesonproportionspart1

# ch25inferencesonproportionspart1 - Chapter 25 Inferences on...

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Chapter 25: Inferences on Proportions (Part 1) A. Dichotomous Population and  Point Estimation of  p There are two types of data: (1) continous data, such as weight, length, (2) discrete data, such as number of rabbits, number of patients. For the former, we assume that the data have a normal population.  Our main interest is in making inferences of  μ. We have studied them before. Now let us look at the latter.  Consider a  dichotomous population , in which each member is either  A or A‘ (ie. non-A).

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We are interested in the parameter p =proportion of A-members If  p  is known, then everything is OK. If  p  is unknown, then we shall take a sample of size  n and count the number of A’s.  Say this is  r Then, we can make inferences on  p . A point estimate of p (see Chapter 14(E)) is: For other inferences such as the interval estimate and the  test of hypotheses, we usually look at cases with large  n. ) 1 ...... ( )......... ( ˆ ortion sampleprop n r p = =

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B. Normal approximation for the Distribution of From the above discussion we see that  r  (the number of A’s  in  n  trials) has a  binomial distribution  (see Chapter 10): Note that  r  is NOT fixed. It is variable taking various values,
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ch25inferencesonproportionspart1 - Chapter 25 Inferences on...

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