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.

1. State the null and alternative hypotheses. Write '≤' as '<=' and '≥' as '>='.
2. In context, explain what the Type I error is.
3. In context, explain what the Type II error is.
4. Which is worse for the patients, a Type I error or a Type II error? Why?

Answer 1

(a)

Ho: The proportion of hip implants that fail is about 0.10 or more (p = ≥ 0.10)

Ha: The proportion of hip implants that fail is less than 0.10 (p < 0.10)

(b)

Type I error: Concluding that the proportion of hip implants that fail is less than 0.10, while in reality it is not

(c)

Type II error: Failing to conclude that the proportion of hip implants that fail is less than 0.10, while in reality it actually is

(d)

Type I error is more serious because the conclusion may lead to launching the new implant design that is not likely to result in fewer failures.