A hypothesis can be rejected at one significance level, but not rejected at another significant level for the same set of samples. The level of significance reflects how much error we can tolerate in the test conclusion. For example, when we buy a 4,000-square-feet house, do you think the measurement is really exact 4,000 square-feet? If you hire 10 people to measure the house, do you think they will give you the same measurement? Then, how do we know the true measurement of the house? What is the proper significant level? If we use different significant levels, what test results do we get?
There are some important principles that we can examine here. The first one has to do with sample size.
In general, the larger the same size, the more chance that our sample will be similar to the true population. In this case above, our 'population' would be the 4000 sq foot measurement.
The 'sample' would be the number of people who come in to measure the house.
So for example, if we have 10 people come into measure our house, we will be 10 slightly different answers. This is due to many things, such as impression of instruments, human error, the shape of the house...
10 people is a small sample. What if 1 of these people made a huge mistake, and said that the house is only 3500 sq ft because they forgot to measure one room? This would be an outlier, and skew the other 9 people's estimates.
If we take the ...
This solution provides assistance with the hypothesis testing problem.