STA215H5 Lecture Notes - Lecture 17: Statistical Hypothesis Testing, Test Statistic
STA215; Chapter 17 - Hypothesis Testing
● One of the purposes of a statistic is to test a hypothesis
● Hypothesis: educated guess about something in the world around you of interest; should
be testable either by experiment of observation
● In hypothesis testing, you are testing whether your results are valid by figuring out the
probability that your results have happened by chance
●EX: MILLIONAIRE
○ Pretend that you are invited to this popular show. As you probably know, you
have to answer a series of multiple choice questions that have four possible
answers to each question. If you don’t know the answer to a question you can
”ask the audience”. Suppose that you run into a question for which you don’t
know the answer with certainty and you decide to ”ask the audience”. You initially
believe that the right answer is A. Then you ask the audience and only 2% of the
audience shares your opinion. What would you do? Change your initial answer or
keep it?
Hypothesis Testing for Proportions
●
●EX: P-VALUE
○ Consider the following hypothesis test:
○ H0: p = 0.75
○ Ha: p < 0.75
○ A sample of 300 items was selected. Compute the p-value and state your
conclusion for each of the following sample results. Use α = 0.05 (5%)
○a) ˆ p = 0.68
■ z* = (phat – pnot)/(root (pnot(1-po))/n)
■ = (0.68 – 0.75)/root (0.75(1-0.75))/300)
■ = -2.80
■ Probability of getting this value or less?
■ p = P(z < z*)
■ p = P(z < -2.80)
■ Small? Probability very unlikely
■ USE TABLE 0.0026
■ Less than 5% chance this will occur reject
Document Summary
One of the purposes of a statistic is to test a hypothesis. Hypothesis: educated guess about something in the world around you of interest; should be testable either by experiment of observation. In hypothesis testing, you are testing whether your results are valid by figuring out the probability that your results have happened by chance. Pretend that you are invited to this popular show. As you probably know, you have to answer a series of multiple choice questions that have four possible answers to each question. If you don"t know the answer to a question you can. Suppose that you run into a question for which you don"t know the answer with certainty and you decide to ask the audience . You initially believe that the right answer is a. Then you ask the audience and only 2% of the audience shares your opinion. A sample of 300 items was selected.
