Problem
23 Salvador Ruiz $\quad$ 07/31/23 7:25 PM (?) 9.2 Question 3, 9.2.17 HW Score: $38.89 \%$, Part 3 of 6 2.33 of 6 points (2) Points: 0.33 of 1 Save A simple random sample of size $\mathrm{n}$ is drawn from a population that is normally distributed. The sample mean, $\bar{x}$, is found to be 114 , and the sample standard deviation, $\mathrm{s}$, is found to be 10 . How does decreasing the sample size affect the margin of error, E? A. As the sample size decreases, the margin of error decreases. B. As the sample size decreases, the margin of error stays the same. C. As the sample size decreases, the margin of error increases. Clear all Final check
Solution
Step 1 ：A simple random sample of size \(n\) is drawn from a population that is normally distributed. The sample mean, \(\bar{x}\), is found to be 114, and the sample standard deviation, \(s\), is found to be 10.
Step 2 ：The margin of error is calculated as the product of the critical value and the standard deviation divided by the square root of the sample size.
Step 3 ：As the sample size decreases, the denominator of this fraction becomes smaller, which in turn makes the overall value of the margin of error larger.
Step 4 ：\(\boxed{\text{C. As the sample size decreases, the margin of error increases.}}\)
