Question

7)- The Department of Highway Improvements, responsible for repairing a 25 mile stretch of interstate highway, wants to design a surface that will be structurally efficient. One important consideration is the volume of heavy freight traffic on the interstate. State weigh stations report that the average number of heavy-duty trailers traveling on a 25 mile segment of the interstate is 72 per hour. However, the section of highway to be repaired is located in an urban area and the department engineers believe that the volume of heavy freight traffic for this particular sector is greater than the average reported for the entire interstate. To validate this theory, the department monitors the high for 50 1-hour periods randomly selected throughout the month. Suppose the sample mean and standard deviation of the heavy freight traffic for the 50 sampled hours are

Sample mean = 74.1 standard deviation = 13.3

a) Do the data support the department’s theory? Use α = 0.10 to come to a conclusion based on a large-sample test.

Answer 1

To test whether the data supports the department's theory of heavy freight traffic volume on the interstate, a large-sample test with α = 0.10 can be used.

Step-by-step explanation:

To test whether the data supports the department's theory, we can use a large-sample test with α = 0.10.

First, we state the null and alternative hypotheses:

Null hypothesis (H0): The average number of heavy freight traffic for this particular sector is not greater than the average reported for the entire interstate.

Alternative hypothesis (H1): The average number of heavy freight traffic for this particular sector is greater than the average reported for the entire interstate.

Next, we calculate the test statistic using the sample mean, population mean, sample standard deviation, and sample size:

Test statistic = (Sample mean - Population mean) / (Sample standard deviation / √Sample size)

Finally, we compare the test statistic to the critical value at α = 0.10. If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the data supports the department's theory.