00:01
All right.
00:01
So prose rhythm is characterized as the occurrence of five -syllable sequences and long passages of text.
00:07
And this characterization can be used to assess the similarity among passages of text and sometimes attending authors.
00:14
And so there's some researchers that looked at plato's republic and found that 26 .1 % of five -syllable sequences are of this type, this five -syllable sequences of this.
00:32
Of the type in which two syllables are short and three syllables are long.
00:37
I suppose the greek archaeologists have found an ancient manuscript dating back to plato's time.
00:42
And a random sample of 317 five syllable sequences from this newly discovered manuscript showed that 61 are of the type, two short and three longs.
00:53
And so we want to know, do the data indicate that the population proportion of this type of five syllable sequence is different, either way, from that of play -dose republic.
01:05
So hypothesis test time.
01:08
So we're going to assume that the p, the popular, or p hat, i should say this.
01:13
I have p in my spreadsheet, but it be p -hath.
01:15
The observed sample minus the, or excuse me, is equal to, sorry, i'm going to jump ahead of myself.
01:27
The observed portion of the sample is equal to that of the population.
01:36
In this case we're assuming this players republic piece 26 .1.
01:40
The alternative hypothesis is that right here it says is different in either way.
01:48
So what we're saying is p hat is not equal to p.
01:53
Nod or p not is the population.
01:58
So let's define those values.
02:00
Well p.
02:00
Not is 0 .261 and p hat is equal to 0 .192, which i got from 602, which i got from 60.
02:08
Divided by 306 or 317 and so this is a one sample z test for proportions so our z for proportions is given as this is where i was jumping into with the hypothesis test here it's p hat minus p not all over the square root of p not times one minus p not all over the sample size so we substitute in the values we have.
02:41
We have everything.
02:43
N is, oh, i didn't define n yet.
02:45
N is 317...