Question

Sue and Javier are working on a statistics project to estimate the proportion of students at their school who have a pet dog. Sue selects a random sample of 81 students from the 2,400 students at their school, and Javier selects a separate random sample of 64 students. They will both construct a 90 percent confidence interval from their estimates. Consider the situation in which the sample proportion from Sue’s sample is equal to the sample proportion from Javier’s sample. Which of the following statements correctly describes their intervals?

Answer 1

the width of sue's interval will be narrower than javier's.

Explanation:

in this problem, i do believe that sue's interval will be more narrow. in the formula,

p-hat ±
`\sqrt{phat(1-phat)/ n` ,

a larger "n" value will lead to a smaller standard error. given that the population proportion is the same for both, and the sample size is the only difference, the standard error of sue's interval will be smaller than javier's, therefore making her whole confidence interval smaller.

again, i do believe this is correct, this is what i have in my AP stat notes. hope this helps!