A biomedical engineer is studying the walking load force, L (measured in Newtons), for a type of hip implant created by the company SupaStrong.

A large-scale clinical trial found that the distribution of L, across the population of SupaStrong hip implant patients, is Gaussian with a mean of 2000 Newtons and a standard deviation of 300 Newtons:

L ~ N(2000,3002).

In the large scale study that was conducted to find that L ~ N(2000,3002), a sample size of 6,400 patients was used. A second, independent sample of size 1600 was used to estimate the distribution of L, which found the distribution to be N(1997,2862).

a. Why is this not a demonstration of the Central Limit Theorem?

b. Describe how the Central Limit Theorem may be demonstrated in the walking load force data that the SupaStrong clinical trials collect.

c. SupaStrong tests one of their implants in a new patient, and finds the patients walking load to be 1200 Newtons. The company makes a statement that says This implant cannot possibly be a SupaStrong implant, as 1200 Newtons is outside the statistical significance level of 5%. What statistical test is SupaStrong implicitly referring to? What is the p-value for the 1200 Newtons data point in this test? What kind of statistical error is the company making by refusing to take responsibility for this implant?