# Z-Test (Z_{0}, Z_{e} & H_{0}) for p_{1} = 0.65 & p_{2} = 0.72 with P Values 0.34 & 0.39

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 difference between two sample proportions p_{1} = 0.65 & p_{2} = 0.72, P values of population *probability *P_{1} = 0.34 & P_{2} = 0.39 for *sample size* n_{1} = 89 & n_{2}= 95
The below is the calculation summary for Z-statistic for the test of significance or hypothesis for difference between two sample proportions p_{1} = 0.65 & p_{2} = 0.72

Calculation Summary | |
---|---|

Sample proportion p_{1} | 0.65 |

Sample proportion p_{2} | 0.72 |

Population probability P_{1} | 0.34 |

Population probability P_{2} | 0.39 |

Sample size n_{1} | 89 |

Sample size n_{2} | 95 |

Z_{0} | 0.9874 |

## Z-Test Work with Steps for p_{1} = 0.65, p_{2} = 0.72

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 difference between two sample proportions p_{1} = 0.65 & p_{2} = 0.72 with known P values of population probability P_{1} = 0.34 & P_{2} = 0.39 for sample size n_{1} = 89 & n_{2}= 95 may help grade school students to solve the similar Z-test statistic (Z_{0}) worksheet problems efficiently.

__Workout :__

step 1 Address the formula input parameters and values

Sample Proportion p

_{1}= 0.65

Sample Proportion p

_{2}= 0.72

Population Probability P

_{1}= 0.34

Population Probability P

_{2}= 0.39

Sample Size n

_{1}= 89

Sample Size n

_{2}= 95

z score value (z) = 0.7

__Formula__

Z

_{0}=p

_{1}- p

_{2}

√

_{1}Q

_{1}) / n

_{1}+ (P

_{1}Q

_{1}) / n

_{2})

step 2 Find Q

_{1}and Q

_{2}from P

_{1}and P

_{2}respectively

Q

_{1}= 1 - P

_{1}

Q

_{1}= 0.66

Q

_{2}= 1 - P

_{2}

Q

_{2}= 0.61

step 3 Substitute p

_{1}, p

_{2}, P

_{1}, P

_{2}, Q

_{1}, Q

_{2}, n

_{1}& n

_{2}value in the below formula for test of significance for difference between two proportion having known P

_{1}& P

_{2}values.

=0.65 - 0.72

√

step 4 Simplify the above expression

=0.07

√

=0.07

√

=0.07

√

=0.07

√

=0.070.0709

Z

_{0}= 0.9874

__Inference__There is significance difference

since the calculated value of Z

_{0}= 0.9874 is greater than the table value of Z

_{e}= 0.7.

Therefore the null hypothesis H

_{0}is rejected.