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education/statistics/Hypothesis Tests.md
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## z tests for percentages ## z tests for percentages
This test can be used if: This test can be used if:
- The data is a simple random sample from the population of interest - The data is a simple random sample from the population of interest
- The sample size is large - The sample size is large ($>30$)
- A qualitative variable of interest summarized by percentages - A qualitative variable of interest summarized by percentages
- Can use a box with tickets of 1s and zeros to represent the population - Can use a box with tickets of 1s and zeros to represent the population
If an observed value is too many SEs away from the expected value, it is hard to explain by chance. If an observed value is too many SEs away from the expected value, it is hard to explain by chance.
@ -23,8 +23,13 @@ Then you can provide a conclusion based off of either the null hypothesis, or th
This test will look very similar to a z test for percentages, it still requires that a large, random, sample was given. This test will look very similar to a z test for percentages, it still requires that a large, random, sample was given.
## t tests for averages ## t tests for averages
This test is used when you have a small sample size (lt 30). This test is used when you have a small sample size ($<30$).
The only major differences used with a *t* test is that you use SD+, and The only major differences used with a *t* test is that you use SD+.
With a small sample size, the standard deviation will be relatively higher, so this is compensated with the $SD_+$.
$$ SD_+ = \sqrt{\frac{size\space sample}{sample\space size}}*SD$$
This found value is then used in all further calculations where you would normally use the $SD$ in a z score test.
$$ t = \frac{obs_{ave} - EV_{ave}}{SE_{ave}} $$
## P Value ## P Value
The chance of observing at least a sample statistic, or something more extreme, if the null hypothesis is true. The chance of observing at least a sample statistic, or something more extreme, if the null hypothesis is true.
If the p-value is less than *5*%, reject the null hypothesis. If the p-value is less than *5*%, reject the null hypothesis.