Question

Number in Family |

7 |

2 |

7 |

3 |

9 |

5 |

5 |

7 |

3 |

4 |

13 |

2 |

6 |

5 |

5 |

4 |

4 |

5 |

3 |

8 |

5 |

2 |

5 |

4 |

7 |

4 |

3 |

4 |

7 |

10 |

4 |

3 |

4 |

4 |

4 |

3 |

6 |

3 |

2 |

3 |

4 |

3 |

7 |

6 |

4 |

2 |

3 |

4 |

4 |

12 |

17 |

4 |

3 |

2 |

3 |

5 |

2 |

4 |

3 |

5 |

5 |

3 |

3 |

5 |

6 |

4 |

3 |

4 |

2 |

3 |

4 |

7 |

5 |

Past enrollment data indicates that 20% of the students taking elementary statistics at FHSU come from families of size three. Is the enrollment in this semester's virtual class significantly different from this claim, as measured statistically? Justify your answer through a formal hypothesis testing procedure on proportions with a 10% level of significance. It is required that you give needed hypotheses and related statistical values below as well as statistical computations to the right (again feel free to use the appropriate template from the Excel Guide for Unit 3). Then give a proper final interpretive conclusion below based on the statistical measures calculated and related to the context given. | |||||||||

H_{0}: |
|||||||||

H_{1}: |
|||||||||

Sample proportion (p-hat): | |||||||||

Critical Value: | |||||||||

Sample's Test Statistic: | |||||||||

P-value: | |||||||||

CONCLUSION: |

Answer #1

The null and alternative hypothesis is

H0: P = 0.20

H1: P
0.20

Count of family size 3 in 73 (x) = 17

Number of objects in a sample provided(n) = 73

No. Of Success Rate ( P )= x/n = 17 / 73 = 0.2329

Test statistic is

Critical Value is

The Value of |Zα| at LOS 0.05% is 1.64

We got |Zo| =0.70 & | Z α | =1.64

Hence Value of |Zo | < | Z α | and Here we Do not Reject
Ho

P-Value: 2*(P > 0.70) = 0.4825

Hence Value of P0.05 < 0.19 324,Here We Do not Reject Ho.

Conclusion: The enrollment in this semester's virtual class NOT significantly different from this claim.

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