Question

a random sample of roosevelt high school students was asked if they prefer taking notes on a computer or using a paper and pencil. of the 180 students who were surveyed, 75 said they preferred using the computer. the resulting 99 percent confidence interval for the proportion of students who prefer taking notes on the computer was (0.322, 0.511).
the school newspaper ran a story saying that less than half of the student body prefers taking notes on a computer.
based on the interval, is the newspaper justified in its statement?
yes. the sample proportion of students who prefer taking notes on their computer was 0.417, which is less than 0.5.
yes. since nearly the entire confidence interval contains values less than 0.5, we can be certain that less than 50% of students prefer using a computer for notes.
no. since the interval contains values above 0.5, it is plausible that more than 50% of students prefer using a computer for notes.
no. since the interval contains values above 0.5, we can be certain that more than 50% of students prefer using a computer for notes.

Explanation:

A 99% confidence interval (0.322, 0.511) means we are 99% confident the true proportion of students preferring computers for notes lies within this range. Since the interval includes values greater than 0.5 (up to 0.511), we cannot rule out that more than half of the student body prefers computers. The newspaper's claim that less than half prefer computers is not justified because the interval does not exclusively contain values below 0.5.

Answer:

No. Since the interval contains values above 0.5, it is plausible that more than 50% of students prefer using a computer for notes.