The 95% confidence limits for P are _________________?
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Answer: D. P±1.96√p2q2/n
Explanation
The 95% confidence interval for population proportion P uses the standard error formula P plus or minus 1.96 times the square root of p squared q squared over n. The value 1.96 corresponds to the critical z-score for a two-tailed 95% confidence level in a normal distribution. This mathematical expression correctly calculates the margin of error required for proportion estimations. Statistical inference relies on confidence intervals to estimate population parameters based on sample statistics. The standard error measures the variability expected when estimating population proportions from random samples. Assuming a normal distribution allows statisticians to use standard z-scores for establishing confidence bounds.
Option A uses an incorrect critical multiplier of 2.18 instead of the standard 1.96 z-score. Option B lacks the square root operation and uses an improper coefficient for standard error. Option C incorrectly places the square root symbol only on the denominator without proper grouping.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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