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Some variations in the Z-test – I


  • What if Christos surveyed the market and found that the student behavior is estimated to be:
    • They would found the training too expensive if their household income is < US$19,000 and hence would not have the buying power for the course?
    • They would perceive the training to be of inferior quality, if their household income is > US$19,000 and hence not buy the training?
    • How would the decision criteria change? What should be the testing strategy?
  • Hint:
    • From the question wording infer: Two tailed testing
    • Appropriately modify the significance value and other parameters
    • Use the Z-test
  • Appropriate change in the decision making and testing process:
    • Students will not attend the course if:
      • The household income >$19,000 and the students perceive the course to be inferior
      • The household income is <$19,000
    • This becomes a two tailed test wherein the student will join the course only when the household lie between a particular boundary. i.e. the household income should be neither very high neither very low

Two – Tailed test


  • Now the test is modified to two-tailed test, which signifies that all z-values that would cause Christos to reject H0, are in both the tails of the sampling distribution
    • μ -> Population Mean
    • H0: μ  = $19,000
    • Ha: μ  ≠ $19,000
  • Since we are checking for significance difference on both the ends, so it’s a two tailed test
  • The lower boundary =
  • Conclusion: If the household income lies between $18,216 and $19,784 then the student will attend the course at 95% confidence

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