Final answer:
The mathematics problem involves testing the instructor's claim that the average length of time to complete homework is 55 minutes using a confidence interval. The null hypothesis is that the mean is 55 minutes, while the alternative hypothesis is that the mean is not 55 minutes.
Step-by-step explanation:
The given problem involves testing a claim related to the mean time students spend on homework using a sample. The sample data has a mean time of 3 hours with a standard deviation of 1.8 hours, and it is known that the population standard deviation is 1.5 hours. A 96% confidence interval will be calculated to test the instructor's claim that the average time to complete the homework is 55 minutes.
To address this problem, we must first state the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis is that the mean time to complete the homework is 55 minutes (μ = 55). The alternative hypothesis is that the mean time is not 55 minutes (μ ≠ 55).
To construct the confidence interval, we would typically calculate the standard error using the population standard deviation, find the z-score that corresponds to a 96% confidence interval, and then create the interval using the sample mean and the standard error multiplied by the z-score.