Lab Assignment 3
Hypothesis Test for Coffee
Hypothesis Test Exercise
This material discusses the basics of hypothesis testing as laid out in chapter 6
Walk through the example hypothesis testing problem shown in these slides to learn the steps and terminology
Then follow those same steps to work through the problem in the MS word document and submit your work to Blackboard by the due date shown on the class schedule for credit
2
Coffee in a Can
A certain coffee manufacturer sells a can of ground coffee beans that says “3 pound can” on the side
We will sample some of their coffee cans and see whether we believe that they really do put 3 pounds of coffee in the can
3
Population Mean and Variation
Although the coffee manufacturer puts the ‘3 pound’ label on the can, not every can contains EXACTLY 3 pounds of coffee
There will be variation from can to can because of the manufacturing process
We are testing whether there is reason to believe that the average weight of the coffee in the population of cans is less than 3 pounds
4
The Hypothesis Test
First, we need to set up Ho and Ha
The thing that we are most interested in showing goes in Ha
Almost always Ho is simply Ha with an equals sign
Ho: ??
Ha: ??
5
Answers for Ho and Ha
Ho: µ=3 pounds
Ha: µ<3 pounds
Where µ is the average of the population
6
Set Alpha
The last thing to do before collecting data is to set the alpha for the test
Alpha is our risk tolerance level
It is our measure of the chances of making a mistake
The form of that mistake is the probability of getting a result from our data that is so unusual that it would only happen alpha percent of the time
When µ is 3
So we set this to be a small number
Almost always .10, .05 or .01 (or 10%, 5%, 1%)
For this problem, we set alpha at 1%
7
Recap
Ho: µ=3 pounds
Ha: µ<3 pounds
Alpha=1%
We set all of this in advance of pulling any data
So now let’s look at the data that we pull
8
Sampled Data
For this experiment we sample 36 cans of coffee and measure how much coffee is in each
The average from these 36 cans is 2.92 pounds
So, n=36 and =2.92
Where is the average from the sample
9
Recap Again
Ho: mu=3 pounds
Ha: mu<3 pounds
Alpha=1%
n=36
=2.92
10
How Unusual?
If Ho is true (that is, if µ=3) how unusual would it be to get an of 2.92
The Central Limit Theorem helps to answer this because it says
~ N (µ, σ/sqrt(n))
What does this mean in words?
11
Calculation for Unusual
We can convert =2.92 to the Z scale and use table A to find out the probability
To do this, we need to know σ [the standard deviation of the population]
For this problem, assume that we know that σ=0.18
So what is the math?
12
The Math (in ugly form)
Z=(-µ)/σ/square root of (n)
Z=(2.92-3)/.18/square root of 36=-2.67
Again, the .18 is an assumption of the problem
13
How Unusual is -2.67?
To find out how unusual -2.67 is, go to Table A
Find the probability of getting a Z of -2.67 or less?
If you don’t have table A, it is available on Blackboard
14
Recap Again!
Ho: µ=3 pounds
Ha: µ<3 pounds
Alpha=1%
n=36
=2.29
σ=0.18
The result of the calculation is z=-2.67
From table A, the probability of a Z of -2.67 or less is 0.0038
15
What Is This Number
The calculated number 0.0038 from this problem is the ___________?
That is, what is the term for this number?
16
Recap Again!
Ho: µ=3 pounds
Ha: µ<3 pounds
Alpha=1%
n=36
=2.29
σ=0.18
The result of the calculation is z=-2.67
From table A, the probability of a Z of -2.67 or less is 0.0038
So the p-value is 0.0038
0.0038 is less than 1%
So we reject Ho for Ha -- Why?
17
Magic Rule #1
Below is the first most important fact for the final exam
If the p-value is less than the alpha, then reject Ho for Ha
0.0038 is less than 0.01 so we rejected Ho
18
Statistical Conclusion, English Conclusion
The statistical conclusion is that we reject Ho for Ha, so we believe that µ is less than 3 pounds
But no one is going to understand this, so we need to put it into plain English
That is not so difficult, simply take Ha and express it in words that were not used in this class …
19
English Conclusion
Ha: µ<3 pounds
This means that the average weight of the population of coffee cans is less than 3 pounds
Add the English conclusion to your hypothesis test problem
Done with the example! Woo-who!
20
Your Turn!
Open the Word document and find a new set of data and a new setting
Execute the calculations and answer the five questions in the Word document
Submit this to the turn-in slot on Blackboard by the due date on the schedule
21