## Question:

How safe are child car seats? Consumer Reports (May 2005) tested the safety of child car seats in 30 mph crashes. They found “slim safety margins” for some child car seats. Suppose that Consumer Reports simulates the safety of the market- leading child car seat. Their test consists of placing the maximum claimed weight in the car seat and simulating crashes at higher and higher miles per hour until a problem occurs. The following data identify the speed at which a problem with the car seat (such as the strap breaking, seat shell cracked, strap adjuster broke, detached from base, etc.) first appeared: 31.0, 29.4, 30.4, 28.9, 29.7, 30.1, 32.3, 31.7, 35.4, 29.1, 31.2, 30.2. Using the facts that the sample mean and sample standard deviation are 30.7833 and 1.7862, respectively, find a 95 percent confidence interval for the population mean speed at which a problem with the car seat first appears. Assume normality. Are we 95 percent confident that this population mean is at least 30 mph?