Final answer:
The 94% confidence interval for the proportion of students who commute is calculated based on the sample proportion and the Z-score for the confidence level. We use a specific formula to find the range that, with 94% confidence, contains the true proportion of commuting students in the population.
Step-by-step explanation:
To calculate the 94% confidence interval for the proportion of students who commute based on a sample where 45% of the students commute, we can use the formula for a confidence interval of a proportion:
CI = π ± Z*(√(π(1-π)/n))
Where π is the sample proportion, Z is the Z-score corresponding to the confidence level, and n is the sample size.
Assuming a normal distribution, we first find the Z-score corresponding to a 94% confidence level using statistical tables or software, then we plug in the values of π (45% or 0.45) and n (100) into the equation to find the margin of error. Finally, we add and subtract the margin of error from the sample proportion to get the confidence interval.
It's worth noting that confidence intervals do not indicate that 94% of the data falls within the interval, but rather that we can be 94% confident that the interval contains the true proportion of the population based on the sample data.