# 5.2 Test your understanding

The following activity will test your understanding of z-scores and your ability to extract data from z-score tables.

## Activity 6 Determine the range of z-scores used to reject a null hypothesis

This activity focuses on assessing your comprehension of z-scores and your ability to extract data from z-score tables. A z-score is a statistical measure that facilitates the comparison of data points from various data sets.

In this activity, you will receive a set of questions that require you to calculate or extract information from z-score tables. To complete this activity successfully, you will need to have a solid grasp of z-scores and their applications. By participating in this activity, you will not only assess your knowledge of z-scores but also refine your problem-solving abilities and capacity to interpret statistical data. Therefore, prepare yourself to challenge your understanding of z-scores in relation to hypotheses testing and enhance your statistical proficiency.

### Part A

Using the z-score table that you created in Activity 5, can you determine the range of z-scores used to reject the null hypothesis?

Alpha levels | z-scores | |
---|---|---|

0.02 | ||

0.04 | ||

0.10 | ||

0.06 | ||

0.07 | ||

0.02 |

Use the free response box below to justify your answers in this exercise.

#### Discussion

Here are the answers:

Alpha levels | z-scores | |
---|---|---|

0.02 (Area left of z: 0.01 and 0.99) |
± 2.33 | |

0.04 (Area left of z: 0.04) |
−1.75 | |

0.10 (Area left of z: 0.90) |
1.28 | |

0.06 (Area left of z: 0.03 and 0.97) |
±1.88 | |

0.07 (Area left of z: 0.07) |
−1.48 | |

0.02 (Area left of z: 0.98) |
2.06 |

### Part B

Using the Excel formula **NORM.S.DIST(z, cumulative)**, can you determine the alpha levels by completing Table 4 below?

Test | z-scores | Alpha levels |
---|---|---|

One-tailed test | 2.35 | |

Two-tailed test | 1.96 | |

One-tailed test | 1.65 | |

Two-tailed test | 1.29 |

#### Comment

There are several things that you need to pay attention to when answering these questions.

- The values indicated in the hypothesis statement will not affect the determination of the z-score.
- The table states the alternative hypothesis, therefore you must translate it into the null hypothesis before answering the question.
- For the two-tailed test, you need to divide the alpha level by 2.
- Alpha levels are stated in the table, so you must translate them to the area left of
*z*before using the z-score table.

Here are the answers

Test | z-scores | Alpha levels |
---|---|---|

One-tailed test | 2.35 | |

Two-tailed test | 1.96 | |

One-tailed test | 1.65 | |

Two-tailed test | 1.29 |