RM - Unit 104 - Null hypothesis testing for a population mean
Book: Analysing Data Using Linear Models
Chapter 2: 2.11, 2.12, 2.13, 2.14, 2.15
Chapter 2.11: Null-hypothesis testing
With null-hypothesis testing, a null hypothesis is stated, after which you decide based on sample data
whether or not the evidence is strong enough to reject that null hypothesis.
Example: the null hypothesis is that the South-African mean has the value 3.38 (the Tanzanian
mean). We write that as follows: H0 : µSA = 3.38. We then look at the data on South-African elephants
that could give us evidence that is either in line with this hypothesis or not. If it is not, we say that we
reject the null hypothesis.
Define regions for sample means where we think the sample mean is no longer probable under the null-
hypothesis and a region where it is probable enough to believe that the null-hypothesis could be true.
For example, we could define an acceptance region where 95% of the sample means would fall if
the null-hypothesis is true, and a rejection region where only 5% of the sample means would fall if the
null-hypothesis is true. Let’s put the get from the sample data is the mean of the sample values. Knowing
the exact values does not give you extra information: the sample mean suffices. The proof for this is
beyond this book. 77 rejection region in the tails of the distribution, where the most extreme values can be
found (farthest away from the mean). We put half of the rejection region in the left tail and half of it in the
right tail of the distribution, so that we have two regions that each covers 2.5% of the sampling
distribution.
The null hypothesis is plausible - if the population mean is 3.28, it is plausible to expect a sample mean
of 3.27 because 95% of random samples we would see a sample mean between 3.255 and 3.500. The
value 3.27 is a very reasonable value and we, therefore, do not reject the null hypothesis.
This is the core of null-hypothesis testing for a population mean:
1. you determine a null-hypothesis that states that the population means to have a certain value
2. you figure out what kind of sample means you would get if the population mean would have that
value
3. you check whether the sample means that you actually have are far enough from the population
mean to say that it is unlikely enough to result from the hypothesized population mean. If that is
Book: Analysing Data Using Linear Models
Chapter 2: 2.11, 2.12, 2.13, 2.14, 2.15
Chapter 2.11: Null-hypothesis testing
With null-hypothesis testing, a null hypothesis is stated, after which you decide based on sample data
whether or not the evidence is strong enough to reject that null hypothesis.
Example: the null hypothesis is that the South-African mean has the value 3.38 (the Tanzanian
mean). We write that as follows: H0 : µSA = 3.38. We then look at the data on South-African elephants
that could give us evidence that is either in line with this hypothesis or not. If it is not, we say that we
reject the null hypothesis.
Define regions for sample means where we think the sample mean is no longer probable under the null-
hypothesis and a region where it is probable enough to believe that the null-hypothesis could be true.
For example, we could define an acceptance region where 95% of the sample means would fall if
the null-hypothesis is true, and a rejection region where only 5% of the sample means would fall if the
null-hypothesis is true. Let’s put the get from the sample data is the mean of the sample values. Knowing
the exact values does not give you extra information: the sample mean suffices. The proof for this is
beyond this book. 77 rejection region in the tails of the distribution, where the most extreme values can be
found (farthest away from the mean). We put half of the rejection region in the left tail and half of it in the
right tail of the distribution, so that we have two regions that each covers 2.5% of the sampling
distribution.
The null hypothesis is plausible - if the population mean is 3.28, it is plausible to expect a sample mean
of 3.27 because 95% of random samples we would see a sample mean between 3.255 and 3.500. The
value 3.27 is a very reasonable value and we, therefore, do not reject the null hypothesis.
This is the core of null-hypothesis testing for a population mean:
1. you determine a null-hypothesis that states that the population means to have a certain value
2. you figure out what kind of sample means you would get if the population mean would have that
value
3. you check whether the sample means that you actually have are far enough from the population
mean to say that it is unlikely enough to result from the hypothesized population mean. If that is
