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)
H0: mu >= 10
Ha: mu < 10

b)
Type I error occurs when one incorrectly rejects the H0.
In this case type I error occurs if we concluded that the number of failures are less than 10 though it is not

c)
Type II error occurs when one incorrectly fails to reject the H0
In this case type II error occurs if we concluded that failures are greater than or equal to 10 though it is less than 10 in reality.

d)
Type II error is worse for the patients because this will lead to rejection of new implant though it is effective