Calculators & Converters

    Z-Test (Z0, Ze & H0) for x̄1 = 78, x̄2 = 85, σ = 9, n1 = 65 & n2 = 75

    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 difference between two sample means1 = 78 & x̄2 = 85, with common population standard deviation σ = 9, and sample size n1 = 65 & n2 = 75. The below is the calculation summary for Z-statistic for the test of significance or hypothesis for difference between two sample means x̄1 = 78 & x̄2 = 85

    Calculation Summary
    Sample mean x̄178
    Sample mean x̄285
    Population Standard deviation σ9
    Sample Size n165
    Sample Size n275
    Z04.5896

    Z-Test Work with Steps for x̄1 = 78 & x̄2 = 85 with common SD

    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 difference between two sample means x̄1 = 78 & x̄2 = 85 with common population standard deviations σ = 9, and sample size n1 = 65 & n2 = 75 may help grade school students to solve the similar Z-test statistic (Z0) worksheet problems efficiently.

    Workout :
    step 1 Address the formula, input parameters and values
    Sample mean x̄1 = 78
    Sample mean x̄2 = 85
    Population Standard deviation σ = 9
    Sample Size n1 = 65
    Sample Size n2 = 75
    z score value (z) = 0.98
    Formula
    Z0=1 - x̄2
    σ
    1/n1 + 1/n2


    step 2 Substitute x̄1, x̄2, σ, n1 & n2 values in the formula

    =78 - 85
    9
    (1 / 65) + (1 / 75)


    step 3 Simplify the above expression
    =7
    9
    (1 / 65) + (1 / 75)


    =7
    9
    0.015384615384615 + 0.013333333333333


    =7
    9
    0.028717948717949


    =79 x 0.1695

    =71.5252

    Z0 = 4.5896

    Inference
    There is significance difference
    since the calculated value of Z0 = 4.5896 is greater than the table value of Ze = 0.98.
    Therefore the null hypothesis H0 is rejected.

    getcalc.com Calculators