hypotheses test when given two populations

Question

I have the following data on duration that different aged adults can remain standing.

Age        Sample Size      Sample Mean      Sample Std Dev
Old         28                801               117
Young       16                780               72

The data I'm using has a normal distribution with the same variances. I want to do a test of hypotheses however at a significance level of 5% (a=0.05) to be able to confirm whether or not the average duration that older adults can remain standing is larger than among younger adults.

I'm not sure which of the different formulas I should use however to determine this due to my sample size being relatively small. Should I be using the following test.

to compute pooled standard deviation: $s^2 = \frac{(1 - 1) s1^2 + (n2 - 1) s2^2}{n1 + n2 -2} $

compute test statistics: $t = \frac{y1 - y2 - 0}{s \sqrt{\frac{1}{n1} + \frac{1}{n2}} } $

Answer 1

In the statement of the problem, you claim that the data have a normal distribution with the same variance. If that's the case, then you should indeed perform a two sample t-test assuming equal variances. The sample size being small is not an issue since you are told the data are normal. Also, since you are told that the variances are the same, you are correct to calculate the pooled standard deviation.