# Some variations in the Z-test â€“ 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 â€“ 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
• Î¼ -> Population Mean
• H0: Î¼  = $19,000 • Ha: Î¼ â‰$19,000
• Since we are checking for significance difference on both the ends, so itâ€™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