# Z-Test (Z_{0}, Z_{e} & H_{0}) for x̄ = 99, μ = 105, σ = 6 & n = 45

Work with steps, formula & calculation summary to estimate the Z-statistic (Z_{0}), critical (table) value (Z_{e}) for degrees of freedom & hypothesis test (H_{0}) 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 x̄ | 99 |

Population mean μ | 105 |

Population standard deviation σ | 6 |

Sample size n | 45 |

Z_{0} | 6.7082 |

## 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 (Z_{0}), critical (table) value (Z_{e}) for degrees of freedom & hypothesis test (H_{0}) 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 (Z_{0}, Z_{e} & H_{0}) 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__

Z_{0}=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.

Z_{0}=99 - 105(6 / √45)

step 3 Simplify the above expression

=6(6 / √45)

=6 x √45 6

=6 x 6.7082 6

Z_{0} = 6.7082

__Inference__

There is significance difference

since the calculated value of Z_{0} = 6.7082 is greater than the table value of Z_{e} = 1.96.

Therefore the null hypothesis H_{0} is rejected.