Final answer:
The null hypothesis for the company's claim is that the failure rate of computer chips in the first 1000 hours is 73%, and the alternative hypothesis suggests it is less than 73%. The hypothesis test is conducted at a 0.10 significance level, with the decision to reject or not reject the null hypothesis based on the p-value as compared to alpha.
Step-by-step explanation:
In the scenario provided, we wish to determine whether the evidence from a sample of 800 computer chips, which shows a 70% failure rate within the first 1000 hours, provides sufficient evidence to dispute the company's claim of a 73% failure rate within the same time frame. To do this, we perform a hypothesis test with a significance level, or alpha, of 0.10.
Null and Alternative Hypotheses
The null hypothesis (H0) proposes that the proportion of computer chips that fail in the first 1000 hours is equal to the claimed proportion, that is, H0: p = 0.73. The alternative hypothesis (H1) suggests that the proportion of failing chips is different from the company's claim, which in this case would be that the proportion is less than claimed: H1: p < 0.73, since the observed failure rate is 70% as opposed to the claimed 73%.
The decision on whether or not to reject the null hypothesis is made based on the p-value of the test statistic. If the p-value is less than the chosen level of significance (alpha), we reject the null hypothesis. If it is greater, we do not reject the null hypothesis.