Download Distributions Used for Hypothesis Tests

Distributions Used for Hypothesis Tests
Normal distribution (Z distributions)
Hypothesis Testing for a Single Population Mean is known = Z-Test
1. You are given the sample standard deviation
2. You are given the population standard deviation
3. The problem deals with means, not percentages
Population standard deviation will always be used to determine the distribution
even if the sample standard deviation is given.
The homework will ask for the z distribution or the distribution written as :
Z ~ N (mean from hypotheses,
𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑎𝑡𝑖𝑜𝑛
√𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒
)
OR
Hypothesis Testing for a Single Population proportion is known = Prop Z-Test
For our class, the only type of hypothesis testing using percentages in the problems
will be Prop Z-Test. They use the normal distributions.
The homework will ask for the z distribution or the distribution written as :
Z ~ P’ (proportion from hypotheses, standard deviation of the proportion (𝜎𝑥 ))
(𝜎𝑥 ) is √
𝑝∗𝑞
𝑛




The p is the proportion used in the hypotheses.
So if the percentage is 5.5%, the proportion is 0.055 which means p = 0.055.
The q is 1 - p so 1 - 0.055 = 0.945.
The n is the sample size which is given in the problem. Let's say it is 100.

To solve it √
𝑝∗𝑞
𝑛
=√
0.055∗0.945
100
= 0.02279 or 0.023
Student’s t-distribution
Hypothesis Testing for Population Means σ is unknown = T-Test
1. You are given the sample standard deviation
2. You are NOT given the population standard deviation
3. The problem deals with means, not percentages
Since the population standard deviation is not given, you have to use the sample
standard deviation.
The homework will ask for the t distribution or the distribution written as :
𝑡𝑑𝑓 where df is degrees of freedom (or sample size -1)