3. Consider the two phrases "fail to reject the null hypothesis" vs. "accept the null hypothesis." If you think about them carefully, these two phrases are very similar. Yet the second is something we never do – we never choose "accept the null hypothesis" as one of the outcomes. Why not? Hint: it may help to use courtroom language instead. In that case, you should discuss the difference between declaring someone "not guilty" and declaring them "innocent."

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 39E: The following problem submitted by Daniel Hahn of Blairstown, Iowa, appeared in the Ask Marilyn...
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hi can you please answer 3 thank you
3. Consider the two phrases "fail to reject the null hypothesis" vs. “accept the null hypothesis." If you
think about them carefully, these two phrases are very similar. Yet the second is something we never do –
we never choose “accept the null hypothesis" as one of the outcomes. Why not?
Hint: it may help to use courtroom language instead. In that case, you should discuss the difference
between declaring someone “not guilty" and declaring them "innocent."
4. Unfortunately it is impossible to avoid making
you will end up tending to make one of the two possible errors more often than the other.
a) By making the null hypothesis the default assumption, which error do you think is more likely to occur
when hypothesis testing – Type I or Type II? Explain briefly.
ors, and depending on how you :
up your system,
b) Our legal system is set up very similarly to hypothesis testing – by making presumption of innocence
the default, we have decided that it is worth sometimes letting a guilty person go free in favor of trying
our best not to convict innocent people. The alternative would be to have a bias toward conviction, so that
we convicted every guilty person but also quite often convicted innocent people too.
Discuss this. Give me your opinion on which error is more dangerous to make and which system works
better, in your opinion.
Transcribed Image Text:3. Consider the two phrases "fail to reject the null hypothesis" vs. “accept the null hypothesis." If you think about them carefully, these two phrases are very similar. Yet the second is something we never do – we never choose “accept the null hypothesis" as one of the outcomes. Why not? Hint: it may help to use courtroom language instead. In that case, you should discuss the difference between declaring someone “not guilty" and declaring them "innocent." 4. Unfortunately it is impossible to avoid making you will end up tending to make one of the two possible errors more often than the other. a) By making the null hypothesis the default assumption, which error do you think is more likely to occur when hypothesis testing – Type I or Type II? Explain briefly. ors, and depending on how you : up your system, b) Our legal system is set up very similarly to hypothesis testing – by making presumption of innocence the default, we have decided that it is worth sometimes letting a guilty person go free in favor of trying our best not to convict innocent people. The alternative would be to have a bias toward conviction, so that we convicted every guilty person but also quite often convicted innocent people too. Discuss this. Give me your opinion on which error is more dangerous to make and which system works better, in your opinion.
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