Which type of variable is required to construct a confidence interval for a $p$ (population proportion)?

"In Problems 23 through 26, indicate whether a confidence interval for a proportion or mean should be constructed to estimate the value of the variable of interest. Justify your response.

Does chewing your food for a longer period of time reduce one’s caloric intake of food at dinner? A researcher requires a sample of 75 healthy males to chew their food twice as long as they normally do. The researcher then records the calorie consumption at dinner."

Explain what “95% confidence” means in a 95% confidence interval.

What type of variable is required to construct a confidence interval for a population proportion?

[NW] You Explain It! New Deal Policies In response to the Great Depression, Franklin D. Roosevelt enacted many New Deal policies. One such policy was the enactment of the National Recovery Administration (NRA), which required businesses to agree to wages and prices within their particular industry. The thought was that this would encourage higher wages among the working class, thereby spurring consumption. In a Gallup survey conducted in 1933 of 2025 adult Americans, 55% thought that wages paid to workers in industry were too low. The margin of error was 3 percentage points with 95% confidence. Which of the following represents a reasonable interpretation of the survey results? For those that are not reasonable, explain the flaw.

b. We are 92% to 98% confident 55% of adult Americans during the Great Depression felt wages paid to workers in industry were too low.

Over the first $20$ days of the semester, one student is late to class on $6$ days. Find the margin of error for a $98\%$ confidence interval for the true proportion of time this student is late.

Over the first $20$ days of the semester, one student is late to class on $6$ days. Construct a $98\%$ confidence interval for the true proportion of time this student is late. 

A previous study found that your school consists of $60\%$ White/Caucasian students. You want the $98\%$ confidence interval for the proportion of White/Caucasian students to be no more than $.05$ away from the true proportion. How many students must you include in a sample to create this confidence interval? 

You wish to estimate with $90\%$ confidence the population proportion of people in Gen-Z that use social media. If you want your estimate to be accurate within $4\%$ of the population proportion, what is the minimum sample size needed?