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Data analysis: hypothesis testing
Data analysis: hypothesis testing

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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

Timing: Allow approximately 45 minutes to complete this activity

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?

Table 3 Calculating z-scores
Alpha levels z-scores
cap h sub a not equals 60 0.02
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cap h sub a less than 12 0.04
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cap h sub a greater than 96 0.10
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cap h sub a not equals 42 0.06
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cap h sub a less than 35 0.07
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cap h sub a greater than 80 0.02
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Words: 0
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Use the free response box below to justify your answers in this exercise.

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Discussion

Here are the answers:

Table 3 Calculating z-scores (completed)
  Alpha levels z-scores
cap h sub a not equals 60 left parenthesis cap h sub zero equals 60 right parenthesis 0.02 (Area left of z: 0.01 and 0.99) ± 2.33
cap h sub a less than 12 left parenthesis cap h sub zero greater than or equals 12 right parenthesis 0.04 (Area left of z: 0.04) −1.75
cap h sub a greater than 96 left parenthesis cap h sub zero less than or equals 96 right parenthesis 0.10 (Area left of z: 0.90) 1.28
cap h sub a not equals 42 left parenthesis cap h sub zero equals 42 right parenthesis 0.06 (Area left of z: 0.03 and 0.97) ±1.88
cap h sub a less than 35 left parenthesis cap h sub zero greater than or equals 35 right parenthesis 0.07 (Area left of z: 0.07) −1.48
cap h sub a greater than 80 left parenthesis cap h sub zero less than or equals 80 right parenthesis 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?

Table 4 Calculating alpha levels
Test z-scores Alpha levels
One-tailed test 2.35
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Two-tailed test 1.96
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One-tailed test 1.65
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Two-tailed test 1.29
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Comment

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

  1. The values indicated in the hypothesis statement will not affect the determination of the z-score.
  2. The table states the alternative hypothesis, therefore you must translate it into the null hypothesis before answering the question.
  3. For the two-tailed test, you need to divide the alpha level by 2.
  4. 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

Table 4 Calculating alpha levels (completed)
Test z-scores Alpha levels
One-tailed test 2.35 tilde operator 0.01
Two-tailed test 1.96 tilde operator 0.01
One-tailed test 1.65 tilde operator 0.05
Two-tailed test 1.29 tilde operator 0.05