You are comparing average weekly customer usage before and after a product change. In the 4 weeks before the change, a random sample of 400 customers averaged 18.6 sessions per week with a standard deviation of 6.2. In the 4 weeks after the change, a separate random sample of 420 customers averaged 19.4 sessions per week with a standard deviation of 6.5. Use a 5% significance level.
Is the observed increase in customer usage statistically meaningful or likely just noise, and how would you justify the decision quantitatively?