Question

7. In 2009, a city planner in Anchorage working on bikeways designed a questionnaire to obtain information about local bicycle commuters. One of the questions asks how long it takes the rider to bike from home to his or her destination. A random sample of 21 local bicycle commuters yielded the following times, in minutes 22 19 24 31 29 29 21 15 27 23 37 31 30 26 16 26 12 23 22 29 28 (a) Illustrate that this dataset is approximately normally distributed, by constructing a relative-frequency histogram using the interval [10, 15) as the first class, the interval [15, 20) as the second class, etc. (b) Find a point estimate for where a denotes the average commute time for all bicycle commuters in Anchorage (c) A point estimate for the standard deviation of the commute times for all bicycle commuters in Anchorage, is given by the sample standard deviation which is 60490 minutes for this dataset Use this value to obtain a 95% confidence interval for (d) Interpret your result in part (c). (e) Ir the confidence level in part(e) is changed to 90% does the confidence interval get narrower or wider? Explain.

Answer 1

(a) The histogram is:

Histogram 35 30 25 20 Percent 15 10 5 0 15 25 35 10 20 30 40 Data

The data is normally distributed.

(b) Average = 24.76

(c) The 95% confidence interval is:

= 24.76 $\pm$ 1.96*(6.0490/$\sqrt{}$21)

= (22.17, 27.35)

(d) We are 95% confident that the true average commute time for all bicycle commuters in Anchorage is between 22.17 and 27.35.

(e) The confidence interval would be narrower because as the confidence level increases, the width increases.