Find the mean number of points for the basketball team and the standard deviation. http://goo.gl/forms/OxRG34i85U
Player Points St. Dev.
John 5 1
Tim 8 2
Ed 12 4
Marcus 10 3
Demetrius 14 4
Inference Test of Difference of Means
Section 11.1
Experiment
Separate – boys & girls.
Take Pulse rates
Remember….
Independent Selection of one sample does not influence
the selection of the other sample
So if we want to estimate the difference in means between two populations…..
The point estimate is:
So
For the difference of means what is the standard deviation?
The properties of the sampling distribution of
If n1 and n2 are sufficiently large or the populations normal, then the distribution will be approximately normal.
1 2x x
1 2x x 1 2
1 2x x
2 21 2
1 2n n
So what is the z-score for the difference in boys and girls pulse rates?
Remember: Use t test if σ is unknown
T-Test statistic 1 2 1 2
2 21 2
1 2
x xt
s s
n n
Use boxplot to check for normal if samples are small & data given.
So is there a difference between boys and girls?
Assumptions:
D.F. is a little more complicated!
22 21 2
1 22 22 2
1 2
1 2
1 21 1
s sn n
dfs sn n
n n
A conservative estimate of the P-value can be found by using a df = smaller of either n1-1 or n2-1.
Let’s try one!
College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this by asking a random sample of 1296 students who had summer jobs how much they earned. They were then separated into two groups based on gender. Is there a difference in the amount males and females earn?
Amounts different for males & females?
n mean st. dev.
Males 675 $1884.52 $1368.37
Females 621 $1360.39 $1037.46
Parameter:
= true mean amount males earned
= true mean amount females earned
1
2
Hypothesis
or
Assumptions
1. Random: samples chosen randomly
2. Approximately normal: n1>30 and n2>30.
3. Independent: more than 6750 males and 6210 females
Name
Use a 2 sample T test of means since σ is unknown
Test Statistic
Obtain a P-value
P-value = tcdf (7.81, ∞., 620)*2 ≈ 0
Now to finish it up!
Make a decision
State a conclusion
Reject the Ho since p-value(0) < α (0.05)
There’s sufficient evidence to support the claim that there is a difference in the amounts earned by males and females.
Pooling the Data
If you prove the standard deviations are equal then you can pool the data together.
You don’t want to do this….it’s another type of hypothesis test to prove standard deviations equal
Never Pool!
The Formula Sheet
If you bought a used camera in good condition from a friend, would you pay the same as you would if you bought the same item from a stranger.
Friend Stranger
275 260
300 250
260 175
300 130
255 200
275 225
290 240
300
Don’t forget the boxplot to show normal!
Homework
Worksheet #1