What are the conditions that must be met for a z confidence interval for a population proportion \( p \)?

A. One random sample AND normal data AND large enough sample size (at least 30).

B. Random selection without repeated measures AND large enough expected counts (all greater than 1, most greater than 5).

C. Normal data AND large enough expected counts (at least 30).

D. One random sample AND normal data or large enough sample size (depending on the extent of departure from normality).

E. One random sample AND large enough counts of successes and failures in the sample (at least 15 each).

The condition that must be met for "z confidence interval" for a "population p" is One random sample AND normal data or large enough sample size , the correct option is (d) .

The conditions for a "z confidence interval" for a "population p" , are Random Sample , Normality , and the Sample Size .

(i) Random sample: The sample must be a random sample from the population of interest, so that the sample proportion is an unbiased estimate of the population proportion.

(ii) Normality: The distribution of the sample proportion must be approximately normal, or the sample size must be large enough for the Central Limit Theorem to apply.

(iii) Sample size: If the sample proportion is near 0 or 1, a larger sample size is needed to ensure that the distribution is approximately normal. In general, a sample size of at least 30 is often considered sufficient to ensure normality.

Therefore, option (d) is the correct answer.

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