1. 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. The impact velocity must be less than 12 meters per second. A European company has just developed a new high impact 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 meters per second. Assume the distribution of impact velocities is normally distributed and that the standard deviation = 0.26
   1. Which level of Type 1 error would you choose, 0.05 or 0.01 and why?
   2. Which kind of statistical test would you use, a one-tailed or two-tailed test?
   3. What are your null and alternative hypothesis?
   4. Conduct your statistical test for alpha = 0.05 and 0.01.
   5. Suppose the population variance, s, was not available and you had to use the sample variance of 0.31. How would this impact your statistical test? If there is a change in your approach, retest your null hypothesis with alpha = 0.5 using your new approach