JESUS CHRIST is the same yesterday, and today, and forever. - Hebrews 13:8

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# Inferential Statistics Calculators I greet you this day,

You may use these calculators to check your answers. You are encouraged to solve the questions first, and check your answers. These topics are covered in my Videos and Notes on Inferential Statistics.

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Samuel Dominic Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S

• Symbols and Meanings
• CL = confidence level or level of confidence or degree of confidence or confidence coefficient
• CI = confidence interval or interval estimate
• α = level of significance or significance level
• zα/2 = critical z value separating an area or probability of α⁄2 in the right tail
• -zα/2 = critical z value separating an area or probability of α⁄2 in the left tail
• zα = critical z value separating an area or probability of α in the right tail
• -zα = critical z value separating an area or probability of α in the left tail
• p̂ = sample proportion or estimated proportion of successes
• q̂ = estimated proportion of failures
• p = population proportion
• SE = standard error
• SEest = estimated standard error
• x = number of individuals in the sample with the specified characteristic
• n = sample size
• N = population size
• E = margin of error or maximum error of estimation or error bound
• x̄ = sample mean
• μ = population mean
• s = sample standard deviation
• s2 = sample variance
• σ = population standard deviation
• σ2 = population variance
• tα/2 = critical t value separating an area or probability of α⁄2 in the right tail (use for one-tailed tests)
• tα = critical t value separating an area or probability of α in the right tail (use for two-tailed tests)
• df = degrees of freedom
• Χ2 = Chi-Square distribution
• Χ2R = right-tailed (upper-tail) critical values of the Chi-Square distribution
• Χ2L = left-tailed (lower-tail) critical values of the Chi-Square distribution
• CI for Population Proportion in Plus-Minus Notation = p̂ ± E
• CI for Population Proportion in Interval Notation = (p̂ - E, p̂ + E)
• CI for Population Proportion in Trilinear Inequality = p̂ - E < p < p̂ + E
• CI for Population Mean in Plus-Minus Notation = x̄ ± E
• CI for Population Mean in Interval Notation = (x̄ - E, x̄ + E)
• CI for Population Mean in Trilinear Inequality = x̄ - E < μ < x̄ + E
• min = minimum data value
• max = maximum data value
• R = range (we shall use it typically for the Range Rule of Thumb)

## Critical Values

#### To Find: α, zα/2

Requirements: population is normally distributed or n > 30 and σ is given

in

#### To Find: CL, zα/2

Requirements: population is normally distributed or n > 30 and σ is given

in

#### To Find: α, critical t

Requirements: population is normally distributed or n > 30 and s is given

in

#### To Find: CL, critical t

Requirements: population is normally distributed or n > 30 and s is given

in

#### To Find: α, critical t

Requirements: population is normally distributed or n > 30 and s is given

in

#### To Find: CL, critical t

Requirements: population is normally distributed or n > 30 and s is given

in

#### To Find: α, critical Χ2

Requirement: population is normally distributed

in

#### To Find: CL, critical Χ2

Requirement: population is normally distributed

in

## Estimating Population Proportion

#### To Find: q̂, E, CI

Requirements: np̂ ≥ 5, nq̂ ≥ 5, np̂q̂ ≥ 10

in

in

#### To Find: p̂, q̂, E, CI

Requirements: np̂ ≥ 5, nq̂ ≥ 5, np̂q̂ ≥ 10

in

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## Estimating Population Mean

in

#### To Find: E, CI

When requirements are met: population is normally distributed or n > 30

in

#### To Find: E, CI

When requirements are met: population is normally distributed or n > 30

in

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