Z-Test (Z0, Ze & H0) for x̄1 = 78, x̄2 = 85, σ = 9, 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 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 x̄1 | 78 |
| Sample mean x̄2 | 85 |
| Population Standard deviation σ | 9 |
| Sample Size n1 | 65 |
| Sample Size n2 | 75 |
| Z0 | 4.5896 |
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.
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=x̄1 - x̄2
σ√
step 2 Substitute x̄1, x̄2, σ, n1 & n2 values in the formula
=78 - 85
9 √
step 3 Simplify the above expression
=7
9 √
=7
9 √
=7
9 √
=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.
