## Preliminary Calculations

Round Preliminary Values to the nearest whole number.

Summary Table for: | Deaths |

Mean | 5,078 |

Median | 4,987 |

Sample Standard Deviation | 3,151 |

Minimum | 1,459 |

Maximum | 15,509 |

Sample Size | 264,039 |

Summary Table for: | Live Births |

Mean | 6,569 |

Median | 6,156 |

Sample Standard Deviation | 4,760 |

Minimum | 1,678 |

Maximum | 25,971 |

Sample Size | 341, 599 |

Summary Table for: | Divorces |

Mean | 4,549 |

Median | 4,063 |

Sample Standard Deviation | 3,547 |

Minimum | 914 |

Maximum | 19,906 |

Sample Size | 236,532 |

Summary Table for: | Marriages |

Mean | 2,291 |

Median | 1,818 |

Sample Standard Deviation | 2,580 |

Minimum | 119 |

Maximum | 10,985 |

Sample Size | 119,110 |

# Hypothesis Testing

With the information that you gather from the Summary Tables above, test the following (you can use excel when appropriate):

## Hypothesis Test #1:

*Determine if there is sufficient evidence to conclude the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance.*

**Step 1: Clearly state a null and alternative hypothesis, identify the claim, and the type of test. (Circle the appropriate symbol or erase the incorrect symbols).**

Ho: μ ≥ ≤ = ________

Ha: μ < > ≠ _________

Circle One: Left Tailed Test Right Tailed Test Two-Tailed Test

**Step 2: Determine the Rejection Region**

Pick **ONE** multiple choice answer below and fill in the critical value. Round Critical Value to two decimal places.

**a) Reject Ho if Z **** ___________**

**b) Reject Ho if Z **** ___________**

**c) Reject Ho if Z is less than ___________ or greater than ___________ .**

**Step 3: Give the value of the test statistic and the P-Value**

Z = _____________ P-Value = ______________

**Step 4: Clearly state your conclusion**

Circle One: Reject the Null Hypothesis….. OR…… Fail to Reject the Null Hypothesis

**Step 5: Explain what your conclusion means in context of the data.**

There _______ (IS/IS NOT) sufficient statistical evidence to ________ (SUPPORT/REJECT) the claim that the average amount of births is _________ (GREATER THAN/LESS THAN/EQUAL TO) 5000 in the United States and territories at the 0.05 level of significance.

## Hypothesis Test #2:

*Determine if there is sufficient evidence to conclude the average amount of deaths is equal to 6000 in the United States and territories at the 0.10 level of significance.*

**Step 1: Clearly state a null and alternative hypothesis, identify the claim, and the type of test. (Circle the appropriate symbol or erase the incorrect symbols).**

Ho: μ ≥ ≤ =

Ha: μ < > ≠

Circle One: Left Tailed Test Right Tailed Test Two-Tailed Test

**Step 2: Determine the Rejection Region**

Pick **ONE** multiple choice answer below and fill in the critical value. Round Critical Value to two decimal places.

**a) Reject Ho if Z **** ___________**

**b) Reject Ho if Z **** ___________**

**c) Reject Ho if Z is less than ___________ or greater than ___________ .**

**Step 3: Give the value of the test statistic and the P-Value**

Z = ___________________ P-Value = _____________________

**Step 4: Clearly state your conclusion**

Circle One: Reject the Null Hypothesis….. OR…… Fail to Reject the Null Hypothesis

**Step 5: Explain what your conclusion means in context of the data.**

There _______ (IS/IS NOT) sufficient statistical evidence to ________ (SUPPORT/REJECT) the claim that the average amount of deaths is _________(GREATER THAN/LESS THAN/EQUAL TO) 6000 in the United States and territories at the 0.10 level of significance.

## Hypothesis Test #3:

*Determine if there is sufficient evidence to conclude the average amount of marriages is greater or equal to 2500 in the United States and territories at the .05 level of significance.*

**Step 1: Clearly state a null and alternative hypothesis, identify the claim, and the type of test. **

Ho: μ ≥ ≤ =

Ha: μ < > ≠

Circle One: Left Tailed Test Right Tailed Test Two-Tailed Test

**Step 2: Determine the Rejection Region**

Pick **ONE** multiple choice answer below and fill in the critical value. Round Critical Value to two decimal places.

**a) Reject Ho if Z **** ___________**

**b) Reject Ho if Z **** ___________**

**c) Reject Ho if Z is less than ___________ or greater than ___________ .**

**Step 3: Give the value of the test statistic and the P-Value**

Z = ____________________ P-Value = ______________________

**Step 4: Clearly state your conclusion**

Circle One: Reject the Null Hypothesis….. OR…… Fail to Reject the Null Hypothesis

**Step 5: Explain what your conclusion means in context of the data.**

There _______ (IS/IS NOT) sufficient statistical evidence to ________ (SUPPORT/REJECT) the claim that the average amount of marriages is _________ (GREATER THAN/LESS THAN/EQUAL TO) 2500 in the United States and territories at the .05 level of significance.

## Hypothesis Test #4:

*Determine if there is sufficient evidence to conclude the average amount of divorces is less than or equal to 4000 in the United States and territories at the 0.10 level of significance.*

**Step 1: Clearly state a null and alternative hypothesis, identify the claim, and the type of test. **

Ho: μ ≥ ≤ =

Ha: μ < > ≠

Circle One: Left Tailed Test Right Tailed Test Two-Tailed Test

**Step 2: Determine the Rejection Region**

**ONE** multiple choice answer below and fill in the critical value. Round Critical Value to two decimal places.

**a) Reject Ho if Z **** ___________**

**b) Reject Ho if Z **** ___________**

**c) Reject Ho if Z is less than ___________ or greater than ___________ .**

**Step 3: Give the value of the test statistic and the P-Value**

Z = ___________________ P-Value= __________________

**Step 4: Clearly state your conclusion**

Circle One: Reject the Null Hypothesis….. OR…… Fail to Reject the Null Hypothesis

**Step 5: Explain what your conclusion means in context of the data.**

There _______ (IS/IS NOT) sufficient statistical evidence to ________ (SUPPORT/REJECT) the claim that the average amount of divorces is _________ (GREATER THAN/LESS THAN/EQUAL TO) 4000 in the United States and territories at the 0.10 level of significance.

## Hypothesis Test #5: Make-Up Your Own Test

Determine if there is sufficient evidence to conclude the average amount of ________________ is _______________________ in the United States and territories at the ________ level of significance.

**Step 1: Clearly state a null and alternative hypothesis, identify the claim, and the type of test. **

Ho: μ ≥ ≤ =

Ha: μ < > ≠

Circle One: Left Tailed Test Right Tailed Test Two-Tailed Test

**Step 2: Determine the Rejection Region**

**ONE** multiple choice answer below and fill in the critical value. Round Critical Value to two decimal places.

**a) Reject Ho if Z **** ___________**

**b) Reject Ho if Z **** ___________**

**c) Reject Ho if Z is less than ___________ or greater than ___________ .**

**Step 3: Give the value of the test statistic and the P-Value**

Z = _______________________ P-Value = ____________________

**Step 4: Clearly state your conclusion**

Circle One: Reject the Null Hypothesis….. OR…… Fail to Reject the Null Hypothesis

**Step 5: Explain what your conclusion means in context of the data.**

There _______ (IS/IS NOT) sufficient statistical evidence to ________ (SUPPORT/REJECT) the claim that the average amount of ________________ is _____________________ (GREATER THAN/LESS THAN/EQUAL TO) ____________ in the United States and territories at the ________ level of significance.

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