Okay, assumption of these are t test, we'll be the assumption is that samples are randomly sample from the population and population is normally distributed. So, I say we mentioned about population and these are sample in Isa, variance and standard deviation. population is the whole the data every data set, and then a sample is is let's say when we use a random sample rain or those are cluster sample rain to get some of the data from the population and sample is a sample support population data so In t test the assumption will be that samples are randomly sample from the population and then the population is normally distributed. So, we are talking about a normally distributed in these descriptive statistics by addressing a population data is normally distributed and a distribution or I will say the histogram will be like a curve or let's say bell curve which I previously show okay should be somewhere here to be something IDs Okay, so the Taiwan errors and type two errors via Taiwan era is a rejection of the null hypothesis when it is really true.

Type two error is that fail to reject Now hypothesis when it is false. Then for t tests we have a T test we have a paired t test, independent t test, then we have a T test is independent, and they receive an equal and then there is a is equal. So, if we look into the future slide, you'll see that the one sample t test, then we have a two sample independent t test and means to sample unpaired t test. So, we have a pair equal to false and then the valence equal to true. Then, we have the two sample unpaired t test when the various are unequal. So, let's see our variance equation false pay equal to false Can we also have a two sample dependent or two sample t test.

So we have our pet equal to true. So we will look into how to get a T test for one sample. So I will copy the code here. So this is the create a data case I don't need to remove all the order sign here. We have our data. So let's say we want to do a one sample t test.

We can do something like t dot test data available one and then the minute 0.6. So let's say T dot s date. Variable one and and many equal to 2.6 K is 0.6. So, we have the p value here. So, this is a T test that is tedious is that we call usually requires a degree of freedom you can use a t statistic and degree of freedom to get a p value. So the p value is 2.2 e to the power minus 60.

So, we can look into let's see how we see the result. So, let's say for our T test or one sample t test, the null hypothesis will be the mean is equal to m 0.6 alternate hypothesis is the mean not equal to n. So, for one sample t test, we will test whether the mean of the data or the mean other data, whether is equal to what we put here 0.6 So, in our one sample t test, our M is 0.6 and in the Bertha arcos so our P value we K is 2.2 e to power minus 60. Our highest p value is less than 0.0 phi is the alpha value. Therefore, we may reject the null hypothesis so we can reject these hypotheses. So, we get a We can see Ah, the test is our alternate hypothesis where the mean of the data in other data is not equal to 0.6