1. Calculate a t-test for the following scenario. An engineer is designing a stationary parts bin at a work table and considers using an established functional grip reach of 29.55 inches taken from the overall population mean, which was published in a textbook. However, the individuals who work in the facility represent a demographic that the engineer has noticed to be a bit small in stature. She decides to take a small sample to test her theory and randomly selects seven individuals and measures their reach. She comes up with the following data: 27.87, 29.49, 28.34, 28.20, 29.00, 29.56, 27.95 (inches). Calculate a mean and sample standard deviation, and use these values to perform a t-test on this data. Report all of these values. Also, discuss the concept of the *p* value and whether the data was significantly different from the population mean. Discuss whether the engineer was correct in assuming the reach of the worker population may be less than the population mean.

Your response should be at least 75 words in length.

2. A review of 200 days-away-from-work injuries for a large, multi-facility corporation was conducted, and it was determined that 18 of them were due to lower back injuries. Only 14.3 were expected under normal conditions. The rest of the injuries were due to other causes where 185.7 were expected. What is the chi-square value? Discuss whether there was a significant difference in observed data vs. the expected data. Also, discuss how the process of hypothesis testing might prove helpful to the safety professional.

Summary of the data:

Observed data: 18 lower back injuries and 182 other injuries

Expected: 14.3 lower back injuries and 185.7 other injuries

Your response should be at least 200 words in length.