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

Thanks for your help!

How did you find the 3.169, please?

To find the 99% confidence interval for the difference between two means, we need to calculate the standard error and then use that to determine the lower and upper limits.

Step 1: Calculate the standard error
The formula for the standard error of the difference between two means is:
SE = √((s1^2 / n1) + (s2^2 / n2))

Where:
s1 and s2 are the standard deviations of the two samples, and
n1 and n2 are the sizes of the two samples.

Given:
Sample 1: Mean = 23, Std. Dev. = 38, Sample Size = 30
Sample 2: Mean = 11, Std. Dev. = 23, Sample Size = 35

Calculating the standard error:
SE = √((38^2 / 30) + (23^2 / 35))

Step 2: Determine the critical value
Since we want to calculate a 99% confidence interval, we need to find the critical value corresponding to a 99% confidence level.

Using a t-distribution, the critical value for a 99% confidence level with conservative degrees of freedom can be found in a t-table or with statistical software. Let’s assume the critical value is 2.66.

Step 3: Calculate the margin of error
The margin of error is given by:
MoE = critical value * standard error

MoE = 2.66 * SE

Step 4: Calculate the lower and upper limits
The lower limit of the confidence interval is given by:
Lower Limit = (sample 1 mean - sample 2 mean) - MoE

Lower Limit = (23 - 11) - MoE

The upper limit of the confidence interval is given by:
Upper Limit = (sample 1 mean - sample 2 mean) + MoE

Upper Limit = (23 - 11) + MoE

Now we can substitute the calculated values into the equations to find the Lower Limit and Upper Limit of the confidence interval.