How do I find the Critical Value?

How do you find the degrees of freedom and critical value using the standard error?

• A commuter wants to determine if Route A is faster than Route B for getting to work. Each day he randomly selects a route to take until he drives each route 15 times. Route A averages 50 minutes with a standard deviation of 3 minutes. Route B takes an average of 53 minutes, with a standard deviation of 3 minutes. Find a 95% confidence level for the difference in mean commuting times between Route B and Route A, UB - UA. I got 1.0954 as my standard error but I don't know how to use this number or the information in the question to get the critical value and the degrees of freedom. Can you tell me how you came up with the answers and how I can do it on Minitab, if possible? Thanks!

• Answer:

  You should re-ask this in Science & Mathematics > Mathematics for more (and likely better) answers. From what I recall, the standard deviation of a difference of independent randoms is the same as that of the sum: sqrt(σ1² + σ2²). That makes the difference 3 min, with a σ of sqrt(18) = 4.24 min Mathworld's table of confidence intervals gives the 95% confidence level at 1.96σ = 8.31 min. So, you have a 95% chance that the true difference UB - UA will be in [3-8.31, 3+8.31] = [-5.31 min, 11.31 min].