Final answer:
Kelly's null hypothesis is that the proportion of returned computers is 7.4% (H₀: p = 0.074), and her alternative hypothesis is that it is higher (Hₐ: p > 0.074). With an alpha of 0.05, if the p-value is less than 0.05, the null hypothesis would be rejected.
Step-by-step explanation:
Kelly is testing the claim that only 7.4% of computers are returned, believing that the true proportion is higher. To do this, she sets up a hypothesis test with an alpha level (α) of 0.05, using a sample size of 285 computers, out of which 25 are returned. We proceed by defining the null and alternative hypotheses. The null hypothesis (H₀) is that the proportion of returned computers is equal to the claimed proportion, H₀: p = 0.074. The alternative hypothesis (Hₐ) is that the proportion of returned computers is greater than the claimed proportion, Hₐ: p > 0.074. The next steps would involve calculating the test statistic using the sample proportion, comparing it to the critical value derived from the standard normal distribution due to the large sample size assumption of normality, and ultimately deciding whether to reject or fail to reject the null hypothesis.
Considering the provided alpha level and sample data, if Kelly finds the calculated p-value to be less than 0.05, she would reject the null hypothesis, concluding that there is sufficient evidence to suggest that the true proportion of returned computers is indeed higher than the company's claim of 7.4%.