Sampling Distribution Calculators

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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

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  • Given: p, p̂, n

    To Find: μ, σp̂, z, detailed P(z)

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  • Given: p, x, n

    To Find: p̂, μ, σp̂, z, detailed P(z)

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

    To Find: σp̂, detailed P(p̂)

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    standard errors the population proportion

  • Given: p, n, a given value from p

    To Find: σp̂, z, detailed P(p̂)

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    the population proportion

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

    To Find: σp̂, z, p̂

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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