In the example we just did, Ann found "that with .95 confidence..." What exactly does "with .95 confidence" mean? The easiest way to understand this is to think about the assumption that Ann had made that she had a sample with a z-score that was not in the tails of the sampling distribution. More specifically, she assumed that her sample had a z-score between ±1.96; that it was in the middle 95 per cent of z-scores. Her assumption is true 95% of the time because 95% of z-scores are between ±1.96. If Ann did this same estimate, including drawing a new sample, over and over, in .95 of those repetitions, the population proportion would be within the interval because in .95 of the samples the z-score would be between ±1.96. In .95 of the repetitions, her estimate would be right.
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