Q 5.154. Suppose that a simple random sam... [FREE SOLUTION]

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Chapter 5: Q 5.154. (page 242)

Suppose that a simple random sample is taken from a finite population in which each member is classified as either having or not having a specified attribute. Fill in the following blanks.
(a) If sampling is with replacement, the probability distribution of the number of members sampled that have the specified attribute is a distribution.
(b) If sampling is without replacement, the probability distribution of the number of members sampled that have the specified attribute is a distribution.
(c) If sampling is without replacement and the sample size does not exceed % of the population size, the probability distribution of the number of members sampled that have the specified attribute can be approximated by a distribution.

Short Answer

Expert verified

Part (a) binomial distribution.

Part (b) hypergeometric distribution.

Part (c) binomial distribution.

Step by step solution

Part (a) Step 1. Given information.

The given statement is:

Suppose that a simple random sample is taken from a finite population in which each member is classified as either having or not having a specified attribute. Fill in the given blanks.

Part (a) Step 2. Fill the blank given in part (a).

It is assumed that the sample will be carried out with replacement.

As we know that a probability distribution will be a binomial distribution if the number of members is taken from a specific attribute (X).

The probability distribution of the number of members sampled who have the stated attribute is a binomial distribution if sampling is performed with replacement.

Part (b) Step 1. Fill the blank given in part (b).

It is assumed that the sample will be done without the use of replacements. It is also assumed that the probability distribution has a certain number of members based on a specific feature.

As a result, the distribution will be hypergeometric.

The probability distribution of the number of members sampled who have the specified attribute is a hypergeometric distribution if sampling is done without replacement.

Part (c) Step 1. Fill the blank given in part (c).

It is assumed that the sampling is carried out without the use of substitutes. In addition, if the sample size is less than 5%, the distribution is a binomial distribution.

The probability distribution of the number of members sampled who have the specified attribute can be approximated by a binomial distribution if sampling is without replacement and the sample size does not exceed 5% of the population size.