Stats hypothesis testing population proportion question Watch

coconut64
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https://imgur.com/a/tde8S

Hi, for this question I am not sure why the sample size is 16 instead of 32 since the populations are involved so why is the total sample size not used?

Also when the H0 is rejected, it is mathematically correct to say H1 is accepted? Or are you not allowed to make this assumption, so you can only say there is sufficient evidence to reject null hypothesis?

Thanks
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Ryanzmw
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I'm confused what you mean about the whole sample size of 32 not being used, it is. 16 in London + 16 in Newcastle. H1 is accepted when H0 fails only if H0 and H1 are mutually exclusive.
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Gregorius
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(Original post by coconut64)
Also when the H0 is rejected, it is mathematically correct to say H1 is accepted? Or are you not allowed to make this assumption, so you can only say there is sufficient evidence to reject null hypothesis?
It depends upon how you've set up the hypothesis test - and it also depends upon style!

The basic guts of a hypothesis test consists in calculating the probability of observing a particular value of a test statistic, given a particular probability model. The probability model is often summarized as a "null hypothesis" - something like "the population mean is zero", whilst taking the rest of the probability model as implicitly granted (for example, the population is normally distributed). And that's all you really need - no mention of an alternative hypothesis here! This was the point of view taken by Fisher, one of the founders of the modern discipline of statistics. At the end of it you either "reject the null hypothesis" or "fail to reject the null hypothesis".

However, two of the other founders of the modern discipline of statistics, Neyman and Pearson, took the view that you should take a positive decision - rather than just rejecting the null hypothesis, they insisted on having an "alternative hypothesis" that was accepted in the case that the null was rejected.

However, this does set up some epistemological questions that I'll leave you to think about. For example compare these two situations

(1) Set up the test so that the null and the alternative partition the possible outcomes (for example, "H0: the mean is zero" versus "H0:the mean is non-zero"
(2) Set up the test so that the null and the alternative do not partition the possible outcomes (for example, "H0: the mean is zero" versus "H1: the mean is one"

How might you differently assess how to interpret the outcome of your test for these two cases?
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I hate maths
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(Original post by Gregorius)
It depends upon how you've set up the hypothesis test - and it also depends upon style!

The basic guts of a hypothesis test consists in calculating the probability of observing a particular value of a test statistic, given a particular probability model. The probability model is often summarized as a "null hypothesis" - something like "the population mean is zero", whilst taking the rest of the probability model as implicitly granted (for example, the population is normally distributed). And that's all you really need - no mention of an alternative hypothesis here! This was the point of view taken by Fisher, one of the founders of the modern discipline of statistics. At the end of it you either "reject the null hypothesis" or "fail to reject the null hypothesis".

However, two of the other founders of the modern discipline of statistics, Neyman and Pearson, took the view that you should take a positive decision - rather than just rejecting the null hypothesis, they insisted on having an "alternative hypothesis" that was accepted in the case that the null was rejected.

However, this does set up some epistemological questions that I'll leave you to think about. For example compare these two situations

(1) Set up the test so that the null and the alternative partition the possible outcomes (for example, "H0: the mean is zero" versus "H0:the mean is non-zero"
(2) Set up the test so that the null and the alternative do not partition the possible outcomes (for example, "H0: the mean is zero" versus "H1: the mean is one"

How might you differently assess how to interpret the outcome of your test for these two cases?
Fascinating post! Such an interesting presentation for a topic that isn't often done justice in the classroom.
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Gregorius
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(Original post by I hate maths)
Fascinating post! Such an interesting presentation for a topic that isn't often done justice in the classroom.
Thank-you! I must admit that I look at my son's A-level stats materials and roll my eyes.
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