Final answer:
To determine the required sample size for a 96% confidence interval with a maximum width of 5.22 hours, one needs the Z-score associated with a 96% confidence level and an estimation of the population standard deviation. The sample size is calculated using the formula that relates these values to the desired interval width.
Step-by-step explanation:
To determine the sample size needed to ensure a 96% confidence interval's width is no more than 5.22 hours when estimating the mean time spent studying by IRSC students, we first need to understand the formula for the width of a confidence interval for a mean which is:
Width of CI = 2 * (Z-score) * (Standard deviation / √n)
The width of the CI is given to be no more than 5.22 hours. The Z-score corresponding to a 96% confidence level can be found using a standard normal distribution table or a Z-score calculator. However, without the population standard deviation, we cannot calculate the exact sample size. If we assumed a value for the standard deviation based on past data or a pilot study, we could then rearrange the formula to solve for the sample size n:
n = (Z-score * Standard deviation / (Width of CI / 2))^2
The formula shows that increasing the Z-score or the standard deviation would require a larger sample size to maintain the same width of the confidence interval. Conversely, a smaller width will also require a larger sample size. Thus, in practice, we first determine the Z-score for a 96% confidence level, estimate a population standard deviation, and then use these values to solve for the sample size that would give us the desired confidence interval width.