Prof. Thistleton STA100 Statistical Methods Lecture 5
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Text Sections: Chapter 4 Sections 1
Basic Probability
One recent semester I gathered the following data on some students:
Gender
Male
Female
Owns a Pet
Yes
15
27
No
6
3
Based upon these data, do you think that there is evidence that men and women own pets at different rates?
How can we develop a theory to answer this sort of a question? Note that we’re not asking whether these
particular men and women own pets at the same rate (since they obviously do not) but whether we can infer
something about the population from which they come.
To answer questions like this we need to know a little probability. As another example, if you and I are flipping
a coin and I receive $1 for Heads while you receive $1 for Tails you might begin to suspect that I’m cheating if
I win 20 times in a row. How about 5 times? 10 times?
To get us started, consider the following experiment. I’ve taken what I believe to be a fair coin and tossed it
10,000 times. Here are my data:
#tosses
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Cumulative
number of
HEADS
509
1012
1513
2016
2488
3015
3545
4050
4565
5059
We can start to notice a few things. First by doing a little subtracting we can see that on the first 1000 tosses I
got 509 heads, on the second I got 503, on the third 501 and so on (503, 472, 527, 530, 505, 515, and 494). Its
impossible to say exactly how many you’ll get on 1000 tosses, but they all seem to be near 500 even though it’s
possible to get as few as 0 and as many as 1.
A simple plot gives us an idea here. If we know that we have obtained 509 heads on the first 1000 tosses then at
this point we have a relative frequency of 509/1000=0.509. In general, define
And then make a plot for our data.
