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Hypothesis testing: one-/two-tailed z-test


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assume that your medical doctor – creating – determiner new truck – on – specific – the – rich and the population – is to keep things simple say six point oh – then you – create – say – number hundred persons – the drug – results – to the spreadsheet – so here's the – pronoun that take determiner horse that pronoun invented – the – meeting – as – determiner – standard – deviation – so – mean – of – five point eight number – standard deviation – oh – five – this looks as though – this little – went down – but on the other hand is huge the – duration – each single way you – goes up and down by approximately – number – the question is how reliable – is to see – the – something – to note up front – this is the litigation – of simple – persons – simple – begin – say okay this – is an integration of the center is – pretty close to the actual standard deviation – that get millions and billions of tax – to proceed statistics is hypothesis – and try – to – reject that hypothesis – six – namely – the hypothesis that you – expected you – to – state determiner six point – oh oh – enough for the treatment – expected – of you means – the average of millions – and billions – of experiments – the next step in statistics – is – to compute – pronoun – number – the data that you got school statistic – that you compute from your experiments – in this case that the things that Z statistic – doings busy test – taking – team that got minus – the expected value – that we publicize – and divide by – standard deviation – divided by the square – number – experiments – extended second – process compute – this – amounts to – the – score – is – minus – six – divided – standard – deviation – to – divide the standard deviation – by the square – number hundred – by – ten – thousand – scores – minus number point eight two – this is – minus – number point eight two – and the basic treatment statistics now is to – check what the benefit is this video occurring given this hypothesis – we try to show – this video is highly improbable – and hence this hypothesis – told – trying to show see what happens – to explain why pronoun formed this strange looking fraction – the – distributions – of these variables – if it's important – if – this hypothesis – is true – start – with the mean – of number hundred measurements – that – pretty – much centered around six – to – look like – actually goes way taller than that – but – to draw this time – if pronoun subtract – six – point oh oh – and – given this hypothesis – it's actually the center of the speed – if pronoun subtract six number oh oh pronoun get it curve that speaks around zero – this is – what – X – bar – minus six point oh oh looks like – the central limit theorem tells us that this girl – space shapes and gets more opaque shaped – as it gets taller – on the – to undo – this effect – is getting tall on – to juice – this – denominator – again this stems from the sublimity of the – dispute – decreases – the square root of the number of measurements – denominator – and us this effect – so – see – the result – has – always the same bed shape independent of the number – of experiments – he has an almost – meeting – zero – and Standard Edition – number – that's – all prediction – if this – is supposed to and on to say – how – improbable – or probabilistic – this – so that this thesis is to – test – pronoun person s pronoun may end up for instance with the video of Munsell on five – and the zebu numeral – nine and that is either – three and sonnets – maybe sometimes – over five or minus number point seven – maybe even – two point number – mostly – in the siege this is what – they should go – to – you – can use the normal distribution – to the – ability – of this video is – actually it's not the ability of precisely this video – minus – number point eight two – because that ability would be zero – to say – this to all verse – something – that's different from zero – control – of his ability – small – the hypothesis that we know something s – wrong – basis – so the scope of his abilities – using the normative solution – just determiner standard patient – our minds number point – eight two – seven – where he – is – even more distant from zero – there is another group of pages – which are as that's on the other side – so plus – number point eight two and – see values which are not – wind – up in pronoun of these regions – we have something – that is – as bad as – to – all works – so what do you say to taste test – eating – old – days – of – next up is to compute the probability – to enter – these – regions – but something began – to – open office – on interested in entity et cetera ability times number hundred – percent – times – this – is the value – to – the – patient pronoun and – get the page shape – such – as to get this integral – as – pronoun accumulated – version – announces – three point four – percent – learn – from that is – that this – amounts to – roughly – three percent – of – the symmetry of the student must – be percent – of the total area – under the bed sheet – looking – at – the rapidity of the value being – in the region – that – will is – three percent plus three percent six percent – best slaughter five percent – percent is the typical threshold for – statistical – significance – and special – so we say it's not – significant – it's something that we could expect – ability is about five percent – it's not determiner rare case – it's something that will – assist you – because it's not significant – can't use this to reject the high offices – so you – this – is pronoun – that aftertreatment – deductible stays – most – this hypothesis – can be rejected – on the basis of the state – let's try second – ellipsis maybe you – this – success – be expected to you is larger than or equal to six point – oh oh so – equals sign – is changed to launder the – the approach is the same this computer – ability – of the – minus number point eight two – verse – the meaning of verse – changed – supplemental – gross distribution – of different actually – know – the distribution – is – if – the expected value was six point oh – see – be distributed – like this – the regular pay shape center at secrets – zero – but it – was seven – this would be the distribution – of Z – shifted – pronoun to the right – if the expected value was – eight – this would be – the distribution – and if the expected value was nine – you – and of course – expected – to be number hundred number thousand twenty four B two point seven – number two – so we do not know which of these curves – which of these distributions – is the pronoun – you know it's pronoun of these – purposes – now have to think of all of this needs to use – minus number point eight or worse – the left-hand side – that's – pretty much whatever before – if – would be if – the expected value is six of the expected value six – discovers – that this distribution – is that it intends – we end up with the battle of minus number which to August didn't – three percent – of the cases – but – if the expected value is six – seven – COO – is not much of it – the resulting validity – of having is the value of minus number point eight two hours would be smaller – even more so for – expected rate of eight or nine – so that he can say – is that this area is three percent at most – determiner specific value we can just say – this area is three percent at most – that's pronoun difference – to the case before – and there is yet another – difference the case before – we end up here plus number point eight two or something – we cannot say anything about that this would be perfect for instance – if the expected value is eight – and – we do not know expected to say so – you simply have to ignore that on – after we got this – is okay – that was either use – above zero – and Soviets begun to anything about the – the softest – is called – wanted – because they just looking – at – pronoun of these – days – of the – date shaped – now comes the important part was the ability – of ending up with – that is either you or verse number – whether this – percent – which is smaller than five percent regular – special – begins – so this is significant – something – has happened – that this – on the improbable – abilities – below five percent – that's determiner significant – and hence – we reject – that ellipsis that this is – let us – to saying that what actually has happened is highly – so – we project that focuses – this – that this doctor does not seem to increase – that – specific