Do your own coin experiment like the one we did
in class.Follow the steps below
and answer all the questions.
1.Find 15 of one of the following types of coins and check which one you are using:
_____Lincoln Memorial pennies (OK, but another type of coin is preferred)
_____Lincoln “wheat”-backed pennies
_____Jefferson nickels
_____Canadian pennies
_____Some other kind of coin that can be balanced on edge
Describe
if other type:______________________________
2. We are doing a test in which the null hypothesis says p=.50 and the alternative is p>.50.Use the binomial table with p=.50and n=15 to obtain greater than or equal to probabilities for all values of x from x=0 to x=15. When you figure out these probabilities, put them in a table, as was done on the class handout for n=20.That is, complete the table below. If you choose Lincoln Memorial pennies or Jefferson nickels, do a test to see if they are more likely to come up Heads than Tails.In this case p represents the true proportion of Heads for Lincoln Memorial pennies (or Jefferson nickels).The test statistic is X = total number of heads.If you choose another type of coin, such as Canadian pennies, do a test to see if these coins are more likely to come up Tails than Heads.In this case the parameter p will represent the true proportion of Tails and the test statistic will be X = total number of tails.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3. Identify
the rejection region for the test.That
is, say what values of would lead us to reject the null hypothesis.)
Reject the null hypothesis if X_______________
4.Carry out the experiment according to the following protocol.
·Find a flat table with a smooth surface.
·Balance all of your coins on edge on the selected surface.Set them upwith random orientations.
·Tap the table surface with a very light vertical blow.The initial blow should be light enough so that few, if any, of the coins fall over.Tap again with a slightly harder vertical blow.Repeat this until all coins have fallen.
·Count
the number of Heads (X) if you are using Lincoln Memorial pennies or Jefferson
nickels.Count the number of Tails
(X) if you are using another type of coin.
Result:X = _____
5.Give
the p-value associated with the value of X that you observed.This
is, give the ³
probability shown in your table for the value of X you gave in Question
4.
p-value = ______
6. Should
the null hypothesis be rejected at a=0.05?That
is, are the results statistically significant at the 5% level? _______
7. If
you tested Lincoln Memorial pennies or Jefferson nickels, do you have convincing
evidence that these coins are unbalanced in favor of Heads? ________If
you tested another type of coin, do you have convincing evidence that this
type of coin is unbalanced in favor of Tails?__________
8. What type of error might you have committed in your response to Questions 6 & 7?
Type I ______Type
II ______Either Type is possible here
_____
9. Do you have any comments regarding your experiment?(For example, if your pet dog wagged its tail and knocked down some of the coins, perhaps the results of the experiment may have been affected.)