Deciding Hypothesis Help

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esrever
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#1
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#1
A bus company agreed to supply a new service if more than 70% people in an area are willing to use it. To test if this is the case, 120 people are questioned about whether they will use the new service. The bus company carries out a test at 2% significance level to decide whether they should run the service.

I thought that the alternate hypothesis will be H_1 : p < 0.7 because the main concern the bus company has is that p may be less than 70%. If p is more than 70%, then there are no issues. But apparently alternate hypothesis is H_1 : p > 0.7. I don't understand why this is the case. So are they regarding null hypothesis as H_0 : p \leq 0.7?
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Gregorius
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#2
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#2
(Original post by esrever)
A bus company agreed to supply a new service if more than 70% people in an area are willing to use it. To test if this is the case, 120 people are questioned about whether they will use the new service. The bus company carries out a test at 2% significance level to decide whether they should run the service.

I thought that the alternate hypothesis will be H_1 : p < 0.7 because the main concern the bus company has is that p may be less than 70%. If p is more than 70%, then there are no issues. But apparently alternate hypothesis is H_1 : p > 0.7. I don't understand why this is the case. So are they regarding null hypothesis as H_0 : p \leq 0.7?
OK, so this is a very poorly worded question, as it assumes a number of things that you're expected to infer from the vague wording!

The basic set-up in hypothesis testing is that there is an "established" position, or opinion, and that you're going to use the data to see whether there's overwhelming evidence that this established position should be abandoned. The hypothesis test is set up so that the established position is the null hypothesis, and you will reject the null hypothesis only if there is enough evidence against it.

So here you are meant to assume that the bus company would rather not put on an extra service; so their null hypothesis will be that p < 0.7, and they will only reject that null if there's enough evidence against it. What you've said is perfectly reasonable: you could reverse the reasoning and say that the bus company would expect to put on the new service (null hypothesis is that p >= 0.7) and only won't if there enough evidence against that.
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esrever
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#3
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#3
(Original post by Gregorius)
OK, so this is a very poorly worded question, as it assumes a number of things that you're expected to infer from the vague wording!

The basic set-up in hypothesis testing is that there is an "established" position, or opinion, and that you're going to use the data to see whether there's overwhelming evidence that this established position should be abandoned. The hypothesis test is set up so that the established position is the null hypothesis, and you will reject the null hypothesis only if there is enough evidence against it.

So here you are meant to assume that the bus company would rather not put on an extra service; so their null hypothesis will be that p < 0.7, and they will only reject that null if there's enough evidence against it. What you've said is perfectly reasonable: you could reverse the reasoning and say that the bus company would expect to put on the new service (null hypothesis is that p >= 0.7) and only won't if there enough evidence against that.
Thank you so much! The idea of established position is very helpful .

But I was always told that the null hypothesis must be a theory of no change. So it must be something like H_0 : p = some constant rather than an inequality like p < 0.7. Is this not true in general?
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Gregorius
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#4
(Original post by esrever)
But I was always told that the null hypothesis must be a theory of no change. So it must be something like H_0 : p = some constant rather than an inequality like p < 0.7. Is this not true in general?
It is not true in general. A null hypothesis like H_0 : p = some constant is what is called a "point null hypothesis"; the reason that you're introduced to this type of null is that it is easy to deal with. When you have a null hypothesis like H_0 : p < 0.7 (called a "compound null hypothesis"), the theory (and practice!) can be much harder.

Indeed, you can make null hypotheses as complicated as you want, depending on the need!
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esrever
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#5
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(Original post by Gregorius)
It is not true in general. A null hypothesis like H_0 : p = some constant is what is called a "point null hypothesis"; the reason that you're introduced to this type of null is that it is easy to deal with. When you have a null hypothesis like H_0 : p < 0.7 (called a "compound null hypothesis"), the theory (and practice!) can be much harder.

Indeed, you can make null hypotheses as complicated as you want, depending on the need!
Makes sense. Thanks!
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Gregorius
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#6
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#6
(Original post by esrever)
But I was always told that the null hypothesis must be a theory of no change.
Oh, and another thing: this statement is very wrong indeed! One use of hypothesis testing is in drug equivalency trials. These are where you have an established treatment, and you wish to test whether an new treatment is "as good as" or "reasonably close to" the old treatment in its effect. For this, the null hypothesis is set up to assume that the difference in effects of the two drugs are greater than a certain set amount and the alternative is that their effect is within that set amount.
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esrever
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#7
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(Original post by Gregorius)
Oh, and another thing: this statement is very wrong indeed! One use of hypothesis testing is in drug equivalency trials. These are where you have an established treatment, and you wish to test whether an new treatment is "as good as" or "reasonably close to" the old treatment in its effect. For this, the null hypothesis is set up to assume that the difference in effects of the two drugs are greater than a certain set amount and the alternative is that their effect is within that set amount.
That's really interesting. So it appears that the idea of hypothesis testing can be greatly extended based on what it is used for.

Thank you so much!
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