Perform a 2 sample non pooled t-test procedure on the summary statistics for 2 independent samples use a significance level of 5%
Sample mean A= 705.375 Sample mean B= 817.067
Sample SD A 183.855 Sample SD B= 330.146
Sample Size A= 8 Sample ize B= 15

I'm assuming that what you are trying test for is whether the means are significantly different from each other. I would recommend using Welch's t-test. That basically is (Mean A - Mean B) / square root ((variance A/sample size A)+(variance B/sample size B))

Variance is the standard deviation squared.

To calculate the degrees of freedom you need the Welch-Satterthwaite equation. I'm going to direct you to this Wikipedia article (Welch's t test - Wikipedia, the free encyclopedia) since I think that will be easier to understand the equation since it is a little complicated to write formulas.

Once you have your t-statistic you can use this site (Free p-Value Calculator for the Student t-Test) to calculate the p-value.

A bank branch located in a commercial district of a city has developed an improved process for serving customers during the 12:00pm to 1:00pm peak lunch period. The waiting time in minutes (operationally defined as the time the customer enters the line to when he or she is served) of all customers during this hour is recoded over a period of one week. A random sample of 15 customers is selected, and the results are as follows:
4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20 4.50 6.10 0.38 5.12 6.46 6.19 3.79

a. Compute the arithmetic mean, median, first quartile, and third quartile, showing your calculations.
b. Compute the standard deviation, range and interquartile range.
as a customer walks into the branch office during the lunch hour, she asks the branch manager how long she can expect to wait. The branch manager replies, ‘Almost certainly not longer than five minutes’. On the basis of the results of (a) and (b), evaluate the accuracy of this statement.