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

The below is the work with step by step calculation shows how to estimate the Z-statistic (Z₀), critical (table) value (Z_e) 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, Z_e & 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 Z_e = 1.96.
Therefore the null hypothesis H₀ is rejected.