Problem: Many environmental groups and politicians are suggesting a return to the federal 55-mile-per-hour (mph) speed limit on Americas highways. They argue that not only will a lower national speed limit reduce greenhouse emissions, it will also increase traffic safety. A researcher believes that a lower speed limit will not increase traffic safety because he feels that traffic safety is based on the variability of the speeds with which people are driving, rather than the average speed. The researcher gathers the speeds of 40 cars from a highway with a speed limit of 55 mph (Highway 1) and the speeds of 40 cars from a highway with a speed limit of 65 mph (Highway 2). A portion of the data is shown in the accompanying table.

a) Calculate the mean and the median for Highway 1.

- Mean:

- Median:

b) Calculate the mean and the median for Highway 2.

- Mean:

- Median:

c) Calculate the standard deviation for Highway 1.

- Standard deviation:

d) Calculate the standard deviation for Highway 2.

- Standard deviation:

e) Does the data support the researchers beliefs?

• Yes, because Highway 1 has a lower typical speed with a higher variability in speed.

• Yes, because Highway 1 has a lower typical speed with a lower variability in speed.

• No, because Highway 2 has a higher typical speed with a higher variability in speed.

• No, because Highway 2 has a lower typical speed with a lower variability in speed.

Car 1 2 Nm Highway 2 60 68 55 66 3 4 Highway 1 60 53 45 66 62 62 67 58 57 5 6 63 73 72 7 8 57 73 9 10 11 12 13 14 75 75 65 76 56 43 53 62 46 59 54 63 53 64 15 16 63 58 76 69 75 76 17 18 19 20 21 22 23 24 25 26 27 41 55 69 71 73 63 65 71 74 57 49 76 55 55 50 61 69 28 29 55 53 43 76 30 60 74 78 31 32 33 34 35 36 45 56 51 58 64 74 66 53 62 37 38 56 76 65 65 47 45 61 39 66 40 74