Transcript AP Statistics Chapter 24 Notes

AP Statistics Chapter 24 Notes
“Comparing Two Sample Means”
New Formulas
SE 
std12 std 22

n1
n2
***USE THE CALCULATOR FOR DEGREES OF FREEDOM***
(n – 1 only applies for 1-sample means
n – 2 can be an approximate estimate)
Hypothesis Testing

A hypothesis test for the difference in the means
of two independent groups tests the null
hypothesis:
m1  m2 , m1  m2  0
o The alternate hypothesis is one of the
following:
m1  m2 , m1  m2  0
m1  m2 , m1  m2  0
m1  m2 , m1  m2  0
Example – with stats

Is there a difference between the resting pulse rates
of males and females? A researcher collected data
from a random sample of US men and women and
found that the average resting pulse rate among the
280 men sampled was 72.75 beats per minute with
a standard deviation of 5.4. The 240 women
sampled had an average resting pulse rate of 70.63
beats per minute with a standard deviation of 7.7.
Is this sufficient evidence to say that there is a
difference between the resting pulse rates of males
and females?
Step-by-Step Solution Process

State the hypotheses

Check the conditions
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Random samples – given information
Independent events – the resting pulse rate of one person is not
influenced by the resting pulse rate of another person
The population of all US men must be at least 2800 men and the
population of all US women must be at least 2400 women.
Since the sample sizes are over 40, we do not have to check a
histogram of each set to make sure it is unimodal and roughly
symmetric. We can proceed on with the testing.
Step-by-Step Solution Process

Perform a two sample t test
(Stat, Tests, #4)
SE 
P  value 
df 

State your conclusion
Confidence Interval (Stat, Tests, #0)
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Find the 95% confidence interval for the difference
between the mean resting pulse rates for the men
and women.
Interpret this interval.

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Based on this sample, we are 95% confident that the mean
resting pulse rate for US men is between _________ and
__________ _____________ than the mean resting pulse
rate for US women.
Does it support your conclusion? Why?