Proportions

Approximately 2.33

Approximately 1.65

Approximately 2.58

Approximately 1.96

We can expect 95% of sample proportions to fall within the interval.

There is a certainty that exactly 95% of the population is described by this interval.

We are 95% confident that the true population proportion falls within the interval.

The population proportion will be in the interval in 95 out of 100 repeated samples.

Employing Bayesian inference with non-informative priors for estimation.

Applying the continuity correction factor to both the upper and lower bounds.

Utilizing bootstrapping techniques to simulate sampling distribution.

Adjusting the standard error by using the adjusted Wald method.

It has no effect as it only applies when samples exceed more than half of the population size.

It leads to wider intervals as it assumes increased uncertainty about parameter estimates in small populations.

It would increase due to higher variability associated with smaller populations.

It would decrease if sampled without replacement from less than 5% of the population.

The sample size can remain unchanged.

The sample size must increase.

The sample size must decrease.

The effect on the sample size cannot be determined without additional information.

It consists entirely of numerical measurements without categories.

It includes outliers only.

The responses are all identical.

That it was randomly selected.

Somewhat Near Estimations Roughly Five Percent Point Range

Large Deviation Greater Than Eight Percentage Points Away From Any Initial Estimates

Regardless of Precision, Any Initial Estimates Are Acceptable As Long As Adjustments Are Made During Actual Collection Phases

Appropriate Close Approximation Within Three Percent Points

Different cumulative probabilities same percentile

Same cumulative probability corresponding percentile

Mean and std.deviation shift to accommodate changes in overall shape of distribution

Same mean and std.deviation regardless whether these correspond to actual underlying distributions

Introduce winsorization processes truncating distribution tails before analysis.

Increasing sample sizes further beyond CLT requirements until empirical rule approximations hold true.

Use quantile regression methods suited toward median-centered parameters.

Applying Tukey's ladder transformation before calculating standard errors.

Coefficient of Variation

Mean Absolute Deviation

Standard error

Sample mean