Part 1: The appropriate test to use in this scenario is a two-sample t-test. This is because we have two independent samples of continuous data (the run times) and we want to compare the means of these samples to determine if there is a significant difference.
Part 2: To find the critical test value, we need to consider the degrees of freedom (df) and the desired level of confidence. Since this is a two-sample t-test, the df can be calculated as follows:
df = (n1 + n2) - 2
where n1 and n2 are the sample sizes. In this case, n1 = 6 and n2 = 8. Plugging these values into the formula, we get:
df = (6 + 8) - 2 = 12
With a desired level of confidence of 95%, we divide the significance level (alpha) by 2 to account for the two tails of the distribution. The remaining probability is split equally between the two tails. Therefore, our alpha value is 1 - (0.95 / 2) = 0.975.
Now, we can find the critical test value using a t-distribution table or a statistical software. For a two-sided test with df = 12 and alpha = 0.975, the critical t-value is approximately 2.178.
Part 3: The calculated test value, also known as the t-statistic, is obtained by comparing the sample means and standard deviations. In this case, we want to compare the mean of route B (93 minutes) to the hypothesized mean of 95 minutes (route A's average). The formula for calculating the t-statistic is as follows:
t = (mean1 - mean2) / sqrt((std1^2 / n1) + (std2^2 / n2))
Plugging in the values, we get:
t = (93 - 95) / sqrt((5.2^2 / 8) + (10.5^2 / 6)) = -0.301
Part 4: Since we are interested in determining if route B is more consistent with a mean of 95 minutes, regardless of being higher or lower, this is indeed a two-tail test. We want to check for any significant difference, not just one specific direction.
Part 5: To determine if we reject or fail to reject the null hypothesis, we compare the calculated test value (t = -0.301) to the critical test value (2.178). If the calculated test value falls outside the range of the critical test value, we reject the null hypothesis.
Given that -0.301 falls within the range of -2.178 to 2.178, we fail to reject the null hypothesis. This means that there is not sufficient evidence to conclude that route B is more consistent with a 95% confidence level.