Dr Who, a cycling fanatic, cycles from her home to work at Macquarie University, a round-trip distance of 13.23 km. She owns two bikes, a road bike and a hybrid bike. She conducted a randomised experiment to see if her commuting time to work depends on which bike she uses. On each of 60 days, she randomly chooses, by flipping a fair one-dollar coin, one of her bikes to ride to work and records the time taken in minutes for each round-trip. CommutingTime.xIsx contains the summary statistics of her commuting time to work and her bike type. Download and use Excel to undertake an appropriate hypothesis test to address the research question. Research Question: On average, were her commuting times in minutes significantly different between the two types of bikes? Figure 1: Road bike Figure 2: Hybrid bike CO co Frequency Frequency O 30 35 40 45 30 35 40 45 Commuting times in minutes Commuting times in minutes Figure 3: Road-Hybrid bike Figure 4: Commuting times Co Commuting times in minutes Frequency 12 13 14 15 16 17 18 Road bike Hybrid bike Differences in commuting timesAnswer the following questions by choosing the most correct option or typing the answer: 1. (1 mark) The most appropriate test for these data is: 2. (1 mark) Which graphical display(s) would be the best to check the normality assumption for this hypothesis? A. Figure 1 B. Figure 2 C. Figure 3 D. Figure 1 & 2 E. Figure 1 & 4 F. Figure 2 & 4 G. Figure 3 & 4 H. No need to check normality assumption I. All four figures are needed 3. (1 mark) How can you check the assumption of equal variances? A. Comparative boxplots could be used B. Descriptive statistics such as variance, standard deviation and range could be used C. Descriptive statistics such as mean and median could be used D. Both A & B could be used E. Both A & C could be used F. No need to check the assumption of equal variances For the remaining questions you may assume that any relevant assumptions have been met. 4. (1 mark) The value of the standard deviation used in calculating the test statistic is minutes (3dp) 5. (2 marks) The absolute value of the test statistic is equal to (3dp) 6. (1 mark) The degrees of freedom is (Integer) 7. (1 mark) The p-value is larger than 0.058. (1 mark) What is the most appropriate conclusion for this test? A. The observed absolute difference 14.883 minutes is statistically significant at the 5% level. B. At the 5% significance level, we do not have enough evidence to reject the null hypothesis, and the round-trip commuting times may be the same for both bike types. C. At the 5% significance level, we accept the null hypothesis, and the round-trip commuting times may be the same for both bike types. 9. Calculate a 95% confidence interval to estimate the mean round-trip commuting times for Dr Who using a road bike. a. (2 marks) The Absolute Value of the Critical Value for this 95% confidence interval is (3dp) b. (2 marks) The range of this 95% confidence interval is minutes (3dp) (Hint: the range is a positive number)