I really need help on this question. I am taking an introductory statistics class, and here is the question:
A taxi company wants to determine if customers will accept self driving cars. The company authorized a survey and subjects were to be selected at random from their current customer database (you can assume independence and a large population). Using the entire customer database, the company determined that the amount paid per trip was normally distributed with a mean of $\$50$ and a standar deviation of $\$5$ and $98\%$ of customers owned a cellphone and $59\%$ of the customers used paypal. The company then selected a simple random sample of size $27$ and conducted in person interviews. Analysis of the sample revealed that the $27$ customers paid an average of $\$53$ with a standard deviation of $\$12$, $47\%$ slept during their ride, and $55\%$ used paypal and 64% are males.
Please construct a $95\%$ confidence interval for the population proportion of customers who slept during their ride.
My question is: why is the question asking for population proportion when the scenario is giving information that indicates I would have to use a t-test for sample means? I am confused whether to use $2.056$ or $1.96$ as the multiplier to construct my confidence interval. I am guessing that I would have to use $1.96$ as my multiplier since the question is asking for population proportion instead of sample means. (and the fact that I would only use the degree of freedom to find my multiplier when they're asking for confidence levels not intervals)?
If any of you guys could approve or disprove my line of thinking, I would greatly appreciate it. Thanks