# Z-Test (Z_{0}, Z_{e} & H_{0}) for p_{1} = 0.75 & p_{2} = 0.85 with unknown P Values

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} = 0.75 & p_{2} = 0.85 with unknown population *probability *for *sample size* n_{1} = 90 & n2= 100. The below is the calculation summary for Z-statistic for the test of significance or hypothesis for difference between two sample proportions p_{1} = 0.75 & p_{2} = 0.85.

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

Sample proportion p_{1} | 0.75 |

Sample proportion p_{2} | 0.85 |

Sample size n_{1} | 90 |

Sample size n_{2} | 100 |

Z_{0} | 1.7291 |

## Z-Test Work with Steps for p_{1} = 0.75, p_{2} = 0.85

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} = 0.75 & p_{2} = 0.85 with unknown P values for sample size n_{1} = 90 & n_{2} = 100 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}= 0.75

Sample Proportion p

_{2}= 0.85

Sample Size n

_{1}= 90

Sample Size n

_{2}= 100

z score value (z) = 0.78

__Formula__

Z

_{0}=p

_{1}- p

_{2}

√

_{1}+ 1 / n

_{2})

step 2 Find estimated proportion

P̄ = n

_{1}p

_{1}+ n

_{2}p

_{2}n

_{1}+ n

_{2}

P̄ = (90 x 0.75 + 100 x 0.85)/(90 + 100)

= (67.5 + 85)/190

= 152.5/190

Probability P̄ = 0.8026

Q̄ = 1 - P̄ = 1 - 0.8026

Q̄ = 0.1974

step 3 Substitute p

_{1}, p

_{2}, P̄, Q̄, n

_{1}& n

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

=0.75 - 0.85

√

step 4 Simplify the above expression

=0.1

√

=0.1

√

=0.1

√

=0.1

√

=0.10.0578

Z

_{0}= 1.7291

__Inference__There is significance difference

since the calculated value of Z

_{0}= 1.7291 is greater than the table value of Z

_{e}= 0.78.

Therefore the null hypothesis H

_{0}is rejected.