Calculators & Converters

    Z-Test (Z0, Ze & H0) for x̄1 = 78, x̄2 = 85, σ1 = 9, σ2 = 11, 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 two different population standard deviations σ1 = 9 & σ2 = 11, 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 σ19
    Population Standard deviation σ211
    Sample Size n165
    Sample Size n275
    Z04.1396

    Z-Test Work with Steps for x̄1=78 & x̄2 = 85 with unequal 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 two different population standard deviations σ1 = 9 & σ2 = 11 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 σ1 = 9
    Population Standard deviation σ2 = 11
    Sample Size n1 = 65
    Sample Size n2 = 75
    z score value (z) = 0.98
    Formula
    Z0=1 - x̄2
    σ12/n1 + σ22/n2


    step 2 Substitute x̄1, x̄2, σ1, σ2, n1 & n2 values in the formula

    =78 - 85
    ((9)2 / 65) + ((11)2 / 75)


    step 3 Simplify the above expression
    =7
    ((9)2 / 65) + ((11)2 / 75)

    =7
    (81/ 65) + (121 / 75)

    =7
    1.2461538461538 + 1.6133333333333

    =7
    2.8594871794872

    =71.691
    Z0= 4.1396

    Inference
    There is significance difference, since the calculated value of Z0 = 4.1396 is greater than the table value of Ze = 0.98. Therefore the null hypothesis H0 is rejected.

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