In a study of red/green color blindness, 850 men and 2500 women are randomly selected and tested. Among the men, 81 have red/green color blindness. Among the women, 5 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.

I calculated 14.85703606 using the formula t=(x1-x2)/sqt s1^2/n1 +s2^2/n2
I am not sure what to do from there to get a 99% confidence interval for the difference between the color blindness rates of men and women

To obtain a 99% confidence interval for the difference between the color blindness rates of men and women, you have correctly calculated the test statistic using the formula t = (x1 - x2) / sqrt[(s1^2 / n1) + (s2^2 / n2)].

However, before proceeding to calculate the confidence interval, let's first check the assumptions required for a t-test:

1. Independent samples: The men and women in the study should be selected randomly and independently.
2. Normality: The number of colorblind individuals in each group (men and women) should follow approximately normal distributions.

Given that you have randomly selected the men and women for the study, and the sample sizes are reasonably large, the assumption of normality can be considered as approximately met.

Now, to calculate the confidence interval, you need the critical value for a 99% confidence level. Since you haven't provided the degrees of freedom for your test statistic, I will assume it is calculated as df = n1 + n2 - 2.

To find the critical value, you can use a t-distribution table or a statistical software. For a 99% confidence level with the assumed degrees of freedom value (df = 850 + 2500 - 2 = 3348), the critical value is approximately 2.61.

Next, you can calculate the standard error (SE) of the difference between the color blindness rates:

SE = sqrt[(s1^2 / n1) + (s2^2 / n2)]

Substituting the given values:
SE = sqrt[(81/850) + (5/2500)]

Once you have the value for SE, the confidence interval can be calculated as follows:

CI = (x1 - x2) ± (t * SE)

Substituting the values:
CI = (81/850 - 5/2500) ± (2.61 * SE)

Now, calculate SE and substitute it into the formula to find the confidence interval.