Question

Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the freeway, resulting in a freer flow of cars, which ultimately results in faster travel times. To test whether ramp metering is effective in reducing travel times, engineers conducted an experiment in which a section of freeway had ramp meters installed on the on-ramps. The response variable for the study was speed of the vehicles. A random sample of 15 cars on the highway for a Monday at 6 p.m. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 p.m. with the meters off resulted in the following speeds (in miles per hour).

Ramp Meters On 29 47 56 39 32 25 42 45 49 35 55 41 42 27 46

Ramp Meters Off 24 26 43 34 38 30 46 37 17 29 24 40 36 50 40

Does there appear to be a difference in the speeds?

A.Yes, the Meters Off data appear to have higher speeds.

B.Yes, the Meters On data appear to have higher speeds.

C.No, the box plots do not show any difference in speeds.

Are there any outliers?

A.Yes, there appears to be a high outlier in the Meters On data.

B.No, there does not appear to be any outliers.

C.Yes, there appears to be a low outlier in the Meters On data.

D.Yes, there appears to be a high outlier in the Meters Off data.

Are the ramp meters effective in maintaining a higher speed on the freeway? Use the alphaαequals=0.01 0.01 level of significance. State the null and alternative hypotheses. Choose the correct answer below.

Determine the P-value for this test.

Choose the correct conclusion

A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms.

State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.

Determine the P-value for this hypothesis test.(round to 3 decimals)

State the appropriate conclusion. Choose the correct answer below.

The data is

Carpeted: 15.3,12.9,10.2,6.9,15.6,12.7,10.6,14.6

Uncarpeted;8.7,10,11.2,10.7,14,6.9,6.4,11.1

Answer 1

(Ramp meters problem)

(a)

Mean speed with ramp meter on = 40.667 and with meter off = 34.267

B.Yes, the Meters On data appear to have higher speeds.

(b)

B.No, there does not appear to be any outliers

(c)

Data:     

n1 = 15    

n2 = 15    

x1-bar = 40.667    

x2-bar = 34.267    

s1 = 9.56    

s2 = 9.16    

Hypotheses:    

Ho: μ1 ≤ μ2    

Ha: μ1 > μ2    

Decision Rule:    

α = 0.01    

Degrees of freedom = 15 + 15 - 2 = 28

Critical t- score = 2.46714009   

Reject Ho if t > 2.46714009   

Test Statistic:    

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] = √(((15 - 1) * 9.56^2 + (15 - 1) * 9.16^2)/(15 + 15 - 2)) = 9.362136508

SE = s * √{(1 /n1) + (1 /n2)} = 9.36213650829766 * √((1/15) + (1/15)) = 3.418568901

t = (x1-bar -x2-bar)/SE = (40.667 - 34.267)/3.41856890135819 = 1.872128421

p- value = 0.03583407   

Decision (in terms of the hypotheses):

Since 1.87212842 < 2.467140089 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that the speeds are higher with the ramp meter on.