Question

A sample of 1600

computer chips revealed that 54%
of the chips fail in the first 1000
hours of their use. The company's promotional literature claimed that below 57%
fail in the first 1000
hours of their use. Is there sufficient evidence at the 0.01
level to support the company's claim?

State the null and alternative hypotheses for the above scenario.

Answer 1

Null hypothesis (Hₒ): The proportion of computer chips failing in the first 1000 hours of use is equal to or higher than 57%.

Alternative hypothesis (Hₐ): The proportion of computer chips failing in the first 1000 hours of use is below 57%.

Mathematically, this can be represented as:

H₀: p ≥ 0.57

Hₐ: p < 0.57

where p represents the true proportion of chips failing in the first 1000 hours.