Find the 99% confidence interval for the difference between two means based on this information about two samples. Assume independent samples from normal populations. (Use conservative degrees of freedom.) (Give your answers correct to two decimal places.)

Sample Number Mean Std. Dev.
1 23 38 30
2 11 23 35

Lower Limit
Upper Limit

(38-23) -+ 3.169* sqrt((30^2/23 +35^2/11)

Lower limit

-23.88

Upper limit
53.88

To find the 99% confidence interval for the difference between two means, we need to use the formula:

Confidence Interval = (X1 - X2) ± Z * √((s1^2 / n1) + (s2^2 / n2))

Where:
- (X1 - X2) is the difference between the means of the two samples.
- Z is the z-score corresponding to the desired confidence level. For a 99% confidence level, the z-score is approximately 2.58.
- s1 and s2 are the standard deviations of samples 1 and 2, respectively.
- n1 and n2 are the sample sizes of samples 1 and 2, respectively.

Let's plug in the given information into the formula:

(X1 - X2) = 23 - 11 = 12
s1 = 38
s2 = 23
n1 = 30
n2 = 35
Z = 2.58

Confidence Interval = 12 ± 2.58 * √((38^2 / 30) + (23^2 / 35))

Now let's calculate the confidence interval:

Confidence Interval = 12 ± 2.58 * √(1444 / 30 + 529 / 35)
Confidence Interval = 12 ± 2.58 * √(48.13 + 15.11)
Confidence Interval = 12 ± 2.58 * √63.24
Confidence Interval = 12 ± 2.58 * 7.95
Confidence Interval = 12 ± 20.49

Lower Limit = 12 - 20.49
Lower Limit = -8.49 (rounded to -8.50)

Upper Limit = 12 + 20.49
Upper Limit = 32.49 (rounded to 32.50)

Therefore, the 99% confidence interval for the difference between the two means is -8.50 to 32.50.