The URL below shows the 4 portraits of Queen Elizabeth II used on Canadian Coins.
Lab 9. will examine the proportion of Canadian pennies or nickles with the portrait:
http://www.mint.ca/store/mint/learn/faces-of-the-monarch-1100026
The question that we wish to examine is: “Is the proportion of Canadian Coins from
1965 to 1989 the same in different piggy banks?”
This may seem silly, but the method would be the same for comparing the incidence
of a disease in different communities in the province.
You are going to see if your coins come from the same population as my coins.
I have 100 coins of which 97 are Canadian.
I will be the second sample. Therefore n2=97.
I have 28 coins with the above portrait. X2=28.
Therefore the sample proportion and the complement are :
28
0.288659794
97
ˆ
q2 1 0.288659794 0.711340206
ˆ
p2
1. State the Null Hypothesis: H0: In terms of the statistics and/or parameters!
The two samples of pennies come from the same populations, and the Alternative
Hypothesis: H1: The two samples of pennies come from different populations.
[ 2 marks ]
H0: ______________________________________ H1: _______________________________
2. Use level of significance = 0.10
3. Make your claim. H0 or H1. Do your coins come from the same population as
mine? State the reason why you have chosen the claim you make.
[ 2 marks ]
4. Count the number of your coins that are Canadian. This will be n 1.______________
All calculations should be shown to all decimal places on the calculator. [ 1 mark ]
5. Count the number of your coins that have the above portrait on them. This will be
X1. __________________________________
[ 1 mark ]
X
ˆ
6. Calculate the proportion of your pennies. p1 n1 ________________________ [ 1 mark ]
1
7. Calculate p
ˆ
ˆ
n p n2 p2
1 1
and q 1 p __________________
n n2
1
_________________
[2
marks ]
8. Calculate the standard error
9. Calculate the test statistic
z
1
1
pq
_______________________
n n2
1
[ 1 mark ]
ˆ ˆ
p1 p2 p1 p2
1 1
pq
n n2
1
_________________________ [ 1 mark ]
The null hypothesis is that p1-p2=0
10. Use either the P-value method or the Critical Area method to accept or reject
the Null Hypothesis.
[3 marks ]
11. State whether there is or is not sufficient evidence to uphold your claim.
[ 1 mark ]
Please number each step as I have above. You do not need to use the symbols to report
each value; you may use the words: p-bar; p-hat; standard error; and alpha etc.
