Statistics 226
Supplemental Instruction
Iowa State University / Leader: / Luyun
Course: / Stat 226
Instructor: / Anna Peterson
Date: / 3/27/16
Statistic tests:
Hypothesis
A hypothesis is a ______about a population parameter that we wish to test.
In any test there are two ______hypotheses:
· The ______, denoted by Ho, is a statement of what we assume to be true.
VS.
· The ______, denoted by Ha, which is a statement against Ho, this is what we want to show.
The philosophy behind a statistical hypothesis test is the same as in the U.S. criminal justice system. There are only two possibilities:
· “not guilty” corresponding to Ho
VS.
· “guilty” corresponding to Ha,
like in a criminal trial, the philosophy is: “innocent until proven guilty.”
That is, we assume “not guilty” until we have enough evidence to determine “guilt”
Likewise, we assume ______until we have sufficient evidence in the data in favor of Ha.
Both, null and alternative hypothesis are always stated in terms of the population parameter. Generally this will be I for us.
In summary we have three different types of alternative hypotheses against the null hypothesis Ho: u=uo, where uo is some pre-specified value that we assume holds true.
1.
3.
Note:
· The “=” sign is always included in the null hypothesis, never in the alternative hypothesis.
· Ho and Ha will always contradict each other.
· uo corresponding to the mean we assume under Ho.
Formulating a hypothesis for each of the following problem descriptions, identify the parameter of interest and formulate an appropriate null and alternative hypothesis.
Example answer:
Parameter of interest: mean amount of fluid in a bottle.
Ho: u= 12 oz
Ha: u≠ 12 oz
(a) a wise owl claims it only takes an average of 3 licks to get to the center of a Tootsie Pop. Fortunately, I have a large collection of Tootsie Pops left over from Halloween and I want to prove the owl wrong.
What is the parameter of interest?
Ho:
Ha:
(b) A clothing retailer recently opened a new location at North Grand Mall. Previous marketing research and corporate experience suggests that the store should be able to survive if mean daily sales are over 800.
What is the parameter of interest?
Ho:
Ha:
(c) Suppose I am monitoring water quality in a stream adjacent to my property. It usually has a pH of 5.9, which is slightly acidie. However, various factors, such as pollutions either from my property or upstream, can increase or decrease this value and I want to know when this happens. For the sake of simplicity, I will say that I do this by taking some samples and testing the mean pH. What are my null and hypothesis.
Ho:
Ha:
(d) Suppose I want to know whether the pH has fallen below 5.6, it has some natural variability, but having an average reading below there would indicate something bad is happening somewhere in the stream. What should the null and alternative hypotheses be now?
Ho:
Ha:
Circle all of the following that make a valid null and alternative hypothesis pair:
(a) Ho: u=10 vs Ha: u > 100
(b) Ho: X=23 vs Ha: X>23
(c) Ho: u=7 vs Ha: u < 7
(d) Ho: u<2 vs Ha: u = 2
(e) Ho: u=1111 vs Ha: u > 1111
(f) Ho: u=17 vs Ha: u ≠ 17
(g) Ho: u = X vs Ha: u> X