Reconsider the sample observations introduced in Exercise 15 in Chapter 2 on the required force (N) to cause initial cracks in a thin enclosure for a subdermally implanted biotelemetry device:
Suppose the device will not be used unless the true average required force to cause initial cracks exceeds 1800 N. Does this requirement appear to have been satisfied? State and test the appropriate hypotheses.
In the article “Mechanical Reliability of Devices Subdermally Implanted into the Young of Long-Lived and Endangered Wildlife” (J. of Materials Engr. and Performance, 2012: 1924–1931), researchers examined the mechanical reliability of a thin enclosure for a biotelemetry device to be subdermally implanted in young wild animals. Six enclosure specimens were subjected to puncture tests. Each specimen was placed in a test apparatus, and researchers recorded the necessary force (N) for the puncture head to cause initial cracks in the enclosure. Here is the corresponding data:
a. Calculate x ~ and the deviations from the mean.
b. Use the deviations calculated in part (a) to obtain the sample variance and the sample standard deviation.
c. Compute the sample standard deviation using a calculator or software function to confirm the accuracy of your answer in (b).