Question

A sample of 1100 computer chips revealed that 58% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 61% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.05 level to dispute the company's claim? State the null and alternative hypotheses for the above scenario.

Answer 1

The null hypothesis is that 61% of computer chips fail in the first 1000 hours of use. The alternative hypothesis is that the percentage is different from 61%. To determine if there is sufficient evidence to dispute the company's claim, we can perform a hypothesis test using a significance level of 0.05.

Step-by-step explanation:

The null hypothesis for this scenario is that 61% of computer chips fail in the first 1000 hours of use. The alternative hypothesis is that the percentage is different from 61%.

To test these hypotheses, we can perform a hypothesis test using a significance level of 0.05. We will calculate the test statistic using the sample proportion and compare it to the critical value from the standard normal distribution.

Since the p-value is not provided, we can determine the p-value by finding the probability of observing the sample proportion of 0.58 or a more extreme value, assuming the null hypothesis is true. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence to dispute the company's claim.