Confidence Intervals
Section 11.1
PANIC
P for Parameter ( 1  2 )
 A for Assumptions – Same as Test
 N for Name of Interval
 I for Interval
 C for conclusion

The average weights of adult male deer in two Colorado regions was
studied. In the Cache la Poudre Region, a sample of 51 deer had an
average weight of 74.04 kg with standard deviation of 17.19 kg. In the
Mesa Verde Region, a random sample of 36 deer gave a mean weight
of 94.53 kg with standard deviation of 19.66 kg. Find a 95% confidence
interval for the difference in the two regions.
P
A
1  mean weight of adult male deer in the Cache la Poudre Region
2  mean weight of adult male deer in the Mesa Verde Region
1  2  Difference in mean weight of the deer
Assumptions
1. Random Samples
2. Approximately normal since n1 > 30 and n2 > 30
3. There are at least 510 deer in Cach and 360 in Mesa..
n
mean
St. Dev.
Cache la Poudre
51
74.04
17.19
Mesa Verde
36
94.53
19.66
2 sample mean T-interval (Use t since σ1 & σ2 are unknown.)
N
I


s12 s22
x1  x 2  t

n1 n2
17.192 19.662

 74.04  94.53  2.042
51
36
20.49  2.042  4.0657 
20.49  8.302
 28.792,
 12.188 
Df = 36-1=35
Interpretation
C
We are 95% confident that the difference in mean
weight of the adult male deer in Cache la Poudre and
the deer in Mesa Verde is between 12.521 and
28.459.
Confidence Intervals can be used
to test data.

Is there evidence that the mean weight of
adult male deer in Cache la Poudre is less
that the mean weight of adult male deer in
Mesa Verde?

Since the entire interval is negative, there’s
sufficient evidence to support the claims that the
Cache la Poudre adult male deer weigh less
than the male deer in Mesa Verde.
We combine the two statements:

We are 95% confident that the difference in mean weight
of the adult male deer in Cache la Poudre and the deer
in Mesa Verde is between 12.521 and 28.459. Since the
entire interval is negative, there’s sufficient evidence to
support the claims that the Cache la Poudre adult male
deer weigh less than the male deer in Mesa Verde.
Brand
Name
Generic
194
205.5
199.2
172.4
184
169.5
190.7
203.5
203.5
206.5
222.5
209.4
The data above shows the average life span of batteries. Is there sufficient
evidence that they are different? Use a 90% confidence interval.
We’re 98% confident that the mean difference in battery life is between
3.885 hrs and 33.295 hrs. In fact, since the entire interval is less than
zero, we can support the claim that the mean life span of the brand name
batteries is less than the mean life span of the generic batteries.
If we are looking at the mean pulse rate of men vs women and find the
confidence interval (-20, 23), how can we interpret this.
Homework

Worksheet #2