Confidence Intervals

Section 11.1

PANIC

P for Parameter ( ) A for Assumptions – Same as Test N for Name of Interval I for Interval C for conclusion

1 2

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 1

2

1 2

mean weight of adult male deer in the Cache la Poudre Region

mean weight of adult male deer in the Mesa Verde Region

Difference in mean weight of the deer

A 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

N 2 sample mean T-interval (Use t since σ1 & σ2 are unknown.)

I

2 21 2

1 2

1 2

2 217.19 19.6674.04 94.53 2.042

51 36

20.49 2.042 4.0657

20.49 8.302

28.792, 12.188

s sx x t

n n

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 194 205.5 199.2 172.4 184 169.5

Generic 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