Calculators & Converters

    Z-Test (Z0, Ze & H0) for x̄ = 99, μ = 105, σ = 6 & n = 45

    Z-Test Calculator

    Work with steps, formula & calculation summary to estimate the Z-statistic (Z0), critical (table) value (Ze) for degrees of freedom & hypothesis test (H0) at a stated level of significance for sample mean x̄ = 99, population mean μ = 105, population standard deviation σ = 6 & sample size n = 45.

    Calculation Summary
    Sample mean x̄99
    Population mean μ105
    Population standard deviation σ6
    Sample size n45
    Z06.7082

    Z-Test Work with Steps for x̄ = 99

    The below is the work with step by step calculation shows how to estimate the Z-statistic (Z0), critical (table) value (Ze) for degrees of freedom & hypothesis test (H0) at a stated level of significance for sample mean x̄ = 99, population mean μ = 105, population standard deviation σ = 6 & sample size n = 45 may help grade school students to solve the similar Z-test (Z0, Ze & H0) worksheet problems efficiently.
    Workout :
    step 1 Address the formula, input parameters and values
    Sample mean x̄ = 99
    Population mean μ = 105
    Population standard deviation σ = 6
    Sample size n = 45

    Z score value (z) = 1.96
    Formula

    Z0=x̄ - μσ/n

    step 2 Substitute sample mean, mean of expectation, sample standard deviation & sample size values in the below Z-test formula to estimate test of significance for large sample mean.

    Z0=99 - 105(6 / 45)

    step 3 Simplify the above expression
    =6(6 / 45)
    =6 x 45 6
    =6 x 6.7082 6
    Z0 = 6.7082

    Inference
    There is significance difference
    since the calculated value of Z0 = 6.7082 is greater than the table value of Ze = 1.96.
    Therefore the null hypothesis H0 is rejected.

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