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## Statistics and probability

### Course: Statistics and probability>Unit 12

Lesson 1: The idea of significance tests

# Comparing P-values to different significance levels

Example comparing P-values to different significance levels, and why it's important to set the significance level before a test.

## Want to join the conversation?

• how do we choose significant level? is there anything that we should use to determine whether to choose a significant level of 0.05, 0.01 or any other value?
• Good question!

It is common to use significance level 0.05, but 0.01 is sometimes used. It depends on the type of real-life situation. The statistician would need to evaluate whether or not lowering the significance level in order to decrease the probability of making a Type I error (the error of rejecting H0 when it's actually true) is worth the cost of increasing the probability of making a Type II error (the error of failing to reject H0 when H0 is false).
• Im getting a different p-value of 0.01586... compared to the 0.036 in the video.

Isnt the formula to calculate p-value

`(0.5^100) * (100 choose 59)`

And that turns out to be (WolframAlpha Link) : https://bit.ly/2xEnp10
• How is the p-value of 0.036 calculated?? time 3.14
• I've tried to calculate that p-value and got different result (0.044313). Here's my question on StackExchange with description of how I got that result: https://math.stackexchange.com/questions/3795024/how-to-manually-calculate-the-p-value-of-getting-at-least-59-heads-in-100-coin-f
Can anyone help?
• n(sample size)=100, p1=.59, p2=.41
st error (of a proportion) = sqrt[(.59)(.41)/100]
z score = (observed-expected rate)/st error
or
z score = (0.59-0.5)/st error = 1.83

Using the z table to look up 1.83 you'll find your answer (will be slightly off because of rounding). You'll have to subtract the looked-up value from 1.
• How do you assume the null hypothesis is true? Do you just say that to yourself? Thanks in advance.
• You ALWAYS assume the null hypothesis is true (for the sake of completing the test). After doing a significance test you reject it or fail to reject it.
• How do you calculate the p-value itself, I didn't find a part in the videos that explained what to actually plug into what equations in this lesson.
• Why does the p-value represent probability of the proportion which is 59% or greater, but not just solely 59%?
• Is there a diagram that shows why we rejected the Ho when P
value is less than significance level for more clarity.