In: Statistics and Probability
What is the purpose of hypothesis testing? Do you see any relevance to hypothesis testing in your daily life?
SOLUTION :-
A hypothesis testevaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data.
The purpose of hypothesis testing is to make a decision in the face of uncertainty. We do not have a fool-proof method for doing this: Errors can be made. Specifically, two kinds of errors can be made: Type I Error: We decide to reject the null hypothesis when it is true.
example of hypothesis testing example 1 :
As you wake up..Panic! What time is it?
Hypothesis (H0): It’s time to get up
Experiment: Carefully open left eye
Data: It’s dark.
Analysis: p-value = P( it’s dark | it’s at least 7am) < 0.05. Would be 0 but small possibility face is still in pillow or world has ended.
Conclusion: Reject H0
Decision: Go back to sleep.
example 2
The school principal wants to test if it is true what teachers say – that high school juniors use the computer an average 3.2 hours a day. What are our null and alternative hypotheses?
h0 : µ = 3.2 Ha : µ1\neq 3.2 Our null hypothesis states that the population has a mean equal to 3.2 hours. Our alternative hypothesis states that the population has a mean that differs from 3.2 hours.
example 3:
We have a medicine that is being manufactured and each pill is supposed to have 14 milligrams of the active ingredient. What are our null and alternative hypotheses?
H0 : µ = 14 Ha : µ1\neq14 Our null hypothesis states that the population has a mean equal to 14 milligrams. Our alternative hypothesis states that the population has a mean that is different than 14 milligrams.