Question

A sample of 1300 computer chips revealed that 28% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 30% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. State the null and alternative hypotheses.

Answer 1

The null hypothesis (νo) states that the actual percentage of computer chips that do not fail in the first 1000 hours is 30% (p = 0.30), while the alternative hypothesis (νa) claims that the percentage is different from the stated 30% (p ≠ 0.30).

Step-by-step explanation:

The student's question pertains to hypothesis testing in statistics, where the quality control manager aims to evaluate the promotional claim for computer chips made by a company. To do this, the null hypothesis (νo) and the alternative hypothesis (νa) must be established.

The null hypothesis (νo) is the statement being tested and is assumed to be true until evidence indicates otherwise. In this case, the null hypothesis is that the actual percentage of chips that do not fail in the first 1000 hours is equal to the stated percentage, which is 30%. It can be formally written as:

νo: p = 0.30

The alternative hypothesis (νa) is what you are testing for, which is the claim that the actual percentage is different from the stated percentage. The alternative hypothesis can be stated as:

νa: p ≠ 0.30