The U.S. Department of Health and Human Services defines “response time” as the time from receipt of a report of child neglect to the initial investigation. Once a call to the agency is received and...

The U.S. Department of Health and Human Services defines “response time” as the time from receipt of a report of child neglect to the initial investigation. Once a call to the agency is received and logged in, the clock starts. Face-to-face contact with the alleged victim marks the initial investigation. There is some concern that workload and poor organization have contributed to a significant increase in the long-term mean response time of 14.0 hours. A random sample of cases was selected, and the response time for each was recorded. Assume s = 3.2 and conduct a hypothesis test to determine whether there is any evidence that the mean response time has increased. Use a = 0.001.

A major cause of injuries in highway work zones is weak construction barriers. One federal government road-barrier specification involves the velocity of a front-seat passenger immediately following impact. This impact velocity must be less than 12 m/s. TSS GmbH, a German company, has just developed a new highimpact road barrier with special absorbing material. In controlled tests the impact velocity was measured for 12 randomly selected crashes. The sample mean was 11.85 m/s. Assume the distribution of impact velocities is normal and s = 0.26.

a. Conduct a hypothesis test to determine whether there is sufficient evidence to suggest the true mean impact velocity is less than 12 m/s. Use a = 0.05.

b. What is your conclusion if a = 0.01?