Question

At a local hospital, the number of hip implants that fail is approximately 10. This number is even higher for women. A new implant design by researchers uses a thinner plastic and will hopefully cause fewer complications and hence reduce the number of additional sugeries. A long-term study was conducted at the hospital to examine the number of failures in men using the new implant design.

a) State the null and alternative hypotheses. Write '≤' as '<=' and '≥' as '>='.

b) In context, explain what the Type I error is.

c) In context, explain what the Type II error is.

d) Which is worse for the patients, a Type I error or a Type II error? Why?

Answer 1

(A) Given that the mean number of hip implants that fail is 10

we have to test whether the new implant design reduces the mean value or not.

So, it is a left tailed hypothesis test

(B) Type I error is defined as the rejection of a true null hypothesis

so, type I error in this case would be given as "concluding that the new implant design reduces the number of hip implants that fails, when in fact the number of hip implants that fails is still 10 or more"

(C) Type II error is defined as the failure to reject a false null hypothesis

so, type II error in this case would be given as "concluding that the new implant design does not reduce the number of hip implants that fails, when in fact the new implant design reduces the number of hip implants that fails"

(D) Type I error is worse for patients because it tells us that the the new implant design reduces the number of hip implants that fails, but it actually does not reduce the failed hip implants. So, type I error will cause severe problems to patience as doctor will declare the hip implant as successful, but it could be a failed hip implant.