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

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.