Confidence Interval Estimation

MCQ on Confidence Interval Estimation based on lecture notes.

Point Estimate

Estimation of a value of a single sample statistic.

Confidence Interval Estimate

A range of numbers constructed around a point estimate, such that the probability that the interval includes the population parameter is known.

Point Estimate

A single number used to estimate a population parameter.

Confidence Interval

Provides additional information about the variability of the estimate; interval estimates.

Confidence Interval Estimate

Gives a range of values, takes into account variation in sample statistics, based on one sample, gives information about closeness to unknown population parameters, stated in terms of level of confidence.

General Formula for Confidence Intervals

Point Estimate ± (Critical Value)(Standard Error)

Point Estimate

The sample statistic estimating the population parameter of interest

Critical Value

A table value based on the sampling distribution of the point estimate and the desired confidence level.

Standard Error

The standard deviation of the point estimate

Confidence Level

The confidence that the interval will contain the unknown population parameter; a percentage less than 100%.

Confidence Interval for μ (σ Known)

If the population standard deviation σ is known, population is normally distributed (or n > 30), then the confidence interval estimate is X̄ ± Zα/2 * (σ/√n).

Critical Value, Zα/2

The value from the normal distribution used in calculating the confidence interval.

Confidence Interval for μ (σ Unknown)

Substitute the sample standard deviation, S, and use the t distribution instead of the normal distribution.

Student’s t Distribution

The t is a family of distributions; the tα/2 value depends on degrees of freedom (d.f.); d.f. = n - 1

Confidence Interval Endpoints for Population Proportion

Upper and lower confidence limits for the population proportion are calculated with the formula p̄ ± Zα/2 * √((p̄(1-p̄))/n)

Confidence Intervals for the Population Proportion, π

An interval estimate for the population proportion (π) can be calculated by adding an allowance for uncertainty to the sample proportion (p).