Hello in this section we're going to start a few one sample tests and in this lecture we will learn
how to perform and interpret the one sample t test again.
Now this test Compares the mean of our sample with a non-value.
Usually the population mean the basic assumptions for the one sample t test are the following the variables.
Today is normally distributed and the variable does not present important outliers in the previous lectures.
We have learned how to check for normality with the SHAPIRO We test and with it gets to them and how
project for outsiders.
So I'm not going to check this again.
Now I'm not going to verify this assumptions.
I let this call you other Natha size.
So let's go further and run the T-test.
I'm going to check whether the average income from this data pray the mall is significantly different
from 70.
So I suppose that the population mean for the income is 70 and I want to verify if the average income
is different from 70 in order to run the TTR.
I'm going to use that T-test Tangshan from the stats package.
In this can I have just fatha tie my variable income from the data they deem all in the alternative
option.
I have answered the two sided value so I want to run a two sided T-test and with the option Ammie you
I introduce my theoretical average my theoretical mean 70 that also that around the T-test.
Now and let's examine.
There is a thought here and the old so with the meaning of my sample here seventy eight point five The
null hypothesis is that this is true.
Mean the observed me if you to 17 and the alternative hypothesis states that the true meaning is not
equal to 70.
Now let's examine the data to see whether we accept or reject the null hypothesis.
The value of the teeth of one point seventy two with five hundred and nine degrees of freedom and the
p value is zero point zero.
A standard p value is higher than 5 percent.
I have to accept the null hypothesis and say that the true mean the mean of the sample is not significantly
different from 70 so it's practically equal to 70.
Finally in the program display the 95 percent confidence interval proof for the Q means.
Sorry it is sixty eight point eight eighty eight point three.
So that talk all the way down to the test.
Thank you.