What critical z-value is used for a 95% confidence interval?

Question

Accepted Answer

1.96. For a 95% confidence interval, the critical z-value is approximately 1.96. This means that 95% of the area under the standard normal curve falls between z = -1.96 and z = 1.96. The confidence interval is calculated as the sample statistic ± 1.96 × (standard error).

The value 1.645 is the critical z-value for a 90% confidence interval, which captures a smaller proportion of the normal distribution. The value 2.576 is the critical z-value for a 99% confidence interval, which is wider to capture a larger proportion. The value 1.28 is approximately the z-value for an 80% confidence interval, which provides less precision.

Knowing the common critical z-values is essential for the DSST exam: 1.645 for 90%, 1.96 for 95%, and 2.576 for 99% confidence. Students should understand that higher confidence levels require larger critical values, resulting in wider intervals. This trade-off between confidence and precision is a fundamental concept in statistical inference.

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