# Sampling Distribution Calculators

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Samuel Dominic Chukwuemeka (SamDom For Peace) B.Eng., A.A.T, M.Ed., M.S ## Sampling Distribution of the Sample Proportion

Condition 1: Simple Random Sample with Independent Trials. If sampling without replacement, N ≥ 10n. Verify that trials are independent: n ≤ 0.05N

Condition 2: Large sample size with at least 10 successes and 10 failures. np ≥ 10 and nq ≥ 10

• Given: p, p̂, n

To Find: q, μ, σ

• in

in

• Given: p, p̂, n

To Find: μ, σp̂, z, detailed P(z)

• in

in

• Given: p, x, n

To Find: p̂, μ, σp̂, z, detailed P(z)

• in

• Given: p, n, the number of standard errors from p

To Find: σp̂, detailed P(p̂)

• in

standard errors the population proportion

• Given: p, n, a given value from p

To Find: σp̂, z, detailed P(p̂)

• in

the population proportion

• Given: p, n, probability less than, probability greater than

To Find: σp̂, z, p̂

• in

The sampling distribution of p̂ is approximately normal if: for n ≤ 0.05N; npq ≥ 10

• Given: n, N, p

To Find: if normal or not, q, μ, σ

## Sampling Distribution of the Sample Mean

Condition 1: Simple Random Sample with Independent Trials. If sampling without replacement, N ≥ 10n. Verify that trials are independent: n ≤ 0.05N

Condition 2: Large sample size where n > 30 or N is normally distributed.

• ### Central Limit Theorem

Given: x, μ, σ, n

To Find: z, detailed P(z), P(x)

• ### Central Limit Theorem

Given: x1, x2 where x1 ≤ x2, μ, σ, n

To Find: z1, z2, detailed P(z), P(x)

• Given: μ, σ, n, the number of standard deviation from μ

To Find: x̄, s, detailed P(x̄)

• standard deviations the population mean

• Given: μ, σ, n, a given value from μ

To Find: x̄, s, z, detailed P(x̄)

• the population mean

• ### Central Limit Theorem

Given: μ, σ, n, probability less than, probability greater than

To Find: z, x̄

• Given: μ, σ, n

To Find: μ , σ