Z-Test (Z0, Ze & H0) for x̄1 = 78, x̄2 = 85, σ1 = 9, σ2 = 11, n1 = 65 & n2 = 75
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 means x̄1 = 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 x̄1 | 78 |
| Sample mean x̄2 | 85 |
| Population Standard deviation σ1 | 9 |
| Population Standard deviation σ2 | 11 |
| Sample Size n1 | 65 |
| Sample Size n2 | 75 |
| Z0 | 4.1396 |
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.
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=x̄1 - x̄2
√
step 2 Substitute x̄1, x̄2, σ1, σ2, n1 & n2 values in the formula
=78 - 85
√
step 3 Simplify the above expression
=7
√
=7
√
=7
√
=7
√
=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.
