1. Katy had two choices of routes to get her to work. She wanted to choose the route that would get her to work fastest, on average. To determine which route would get her to work faster, on average, she randomly selected 10 days and took Route 1 on those 10 days. Then she randomly selected a different 10 days and took Route 2 on those 10 days. She recorded the time, in minutes, it took her to get from her house to work on each of those 20 days. From her data, she constructed the 95% confidence interval for the difference in mean commuting times (Route 1-Route 2) in minutes as (-1,9) Based on this confidence interval, which of the following is a correct statement? A. There is evidence at the 5% significance level to indicate that one route gets Katy to work faster, on average, since one bound is close to 0
B. There is not enough evidence at the 5% significance level to indicate that the average commuting times for the two routes is the same
C. There is evidence at the 5% significance level to indicate that one route gets Katy to work faster, on average, since 0 falls between the bounds of the confidence interval.
D. There is not enough evidence at the 5% significance level to indicate that one route gets Katy to work faster, on average, since 0 falls within the bounds of the confidence interval
2. Katy had two choices of routes to get her to work. She wanted to choose the route that would get her to work fastest, on average. To determine which route would get her to work faster, on average, she randomly selected 10 days and took Route 1 on those 10 days. Then she randomly selected a different 10 days and took Route 2 on those 10 days. She recorded the time, in minutes, it took her to get from her house to work on each of those 20 days. Katy wanted to construct a confidence interval for the difference in population means using the two-sample t-methods. Which of the following statements is true regarding the conditions that must be met for Katy to use the two-sample t-methods for inference in this problem?
A. Since both sample sizes are small the distribution of the difference in sample means will not be normal regardless of the shape of the distributions of all commuting times for both routes.
B. Since both sample sizes are small. Katy would have to believe that all commuting times for both routes are normally distributed in order for the distribution of the difference in sample means to be normal.
C. Because the sample of days to take route 1 and route 2 were chosen randomly, the distribution of the difference in sample means will be approximately normal.
D. Since both sample sizes are small Katy would have to believe that all commuting times for both routes are normally distributed in order for the commuting times used in the samples to be representative of all commuting times for both routes