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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