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The conditions for a sampling distribution of a sample proportion, when you do not know the true proportion, are:

A. Randomization, 10% Condition, Success/Failure Condition

B. Randomization, 10% Condition, Nearly Normal Condition

C. Randomization, 10% Condition, Nearly Normal Condition, Independent Groups, Large Enough Condition

D. Randomization, 10% Condition, Count Data, Expected Value Condition

Answer :

The conditions for a sampling distribution of a sample proportion, when the true proportion is unknown, are (b) Randomization, 10% Condition, Nearly Normal Condition.

The conditions for a sampling distribution of a sample proportion are important in statistical inference when dealing with categorical data. They ensure that the sampling distribution approximates a normal distribution, allowing for valid statistical tests and confidence intervals.

(a) Randomization: The sampling must be done randomly to ensure that the sample is representative of the population and reduces bias.

(b) 10% Condition: The sample size should be no more than 10% of the population size to ensure that the sampling distribution can be approximated by the binomial or normal distribution.

(c) Nearly Normal Condition: The sample should be sufficiently large to satisfy the nearly normal condition. If the sample size is large enough, the sampling distribution of the sample proportion can be approximated by a normal distribution, even if the population distribution is not normal.

(d) Independent Groups: The samples should be independent, meaning that the observations within each sample are not influenced by the other samples.

Therefore, the correct answer is (b) Randomization, 10% Condition, Nearly Normal Condition. These conditions are necessary to ensure valid statistical inference when working with sample proportions.

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