Question

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... 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.

Answer 1

= (27.87 + 29.49 + 28.34 + 28.20 + 29 + 29.56 + 27.95)/7 = 28.63

s = sqrt(((27.87 - 28.63)^2 + (29.49 - 28.63)^2 + (28.34 - 28.63)^2 + (28.20 - 28.63)^2 + (29 - 28.63)^2 + (29.56 - 28.63)^2 + (27.95 - 28.63)^2)/7) = 0.66

H₀: = 29.55

H₁: < 29.55

The test statistic t = ()/(s/sqrt(n))

                             = (28.63 - 29.55)/(0.66/sqrt(7))

                             = -3.688

DF = 7 - 1 = 6

P-value = P(T < -3.688)

             = 0.0051

At 0.05 significance level, as the P-value is less than the significance level (0.0051 < 0.05), so the null hypothesis is rejected.

So we can conclude that the engineer was correct in assuming the reach of the worker population may be less than the population mean.