Question

Arthur is conducting a study on the preferred study options of students from East County College. He randomly selected 32 students from the college, and found that 25% of those surveyed preferred studying abroad. Assuming a 95% confidence level, which of the following statements holds true?

A. As the sample size is too small, the margin of error cannot be trusted.
B. As the sample size is too small, the margin of error is ±0.15.
C. As the sample size is appropriately large, the margin of error is ±0.178.
D. As the sample size is appropriately large, the margin of error is ±0.15.​

Answer 1

D. As the sample size is appropriately large, the margin of error is ±0.15

Explanation:

The number of students in the sample, n = 32 students

The percentage of the students that preferred studying abroad,
`\hat p` = 25%

The confidence level for the study = 95%

As a general rule, a sample size of 30 and above are taken as sufficient

The z-value at 95% confidence level, z = 1.96

The margin of error of a proportion formula is given as follows;

`M.O.E. = z^** \sqrt{\frac{\hat{p} \cdot(1-\hat{p})}{n}}`

Therefore, we get;

`M.O.E = 1.96* \sqrt{(0.25*(1-0.25))/(32)} \approx \pm0.15`

Therefore, the correct option is that as the sample size is appropriately large, the margin of error is ±0.15.