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, $\mathrm{s}$, is found to be 10 . Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, $E$ ? A. As the level of confidence decreases, the size of the interval stays the same. B. As the level of confidence decreases, the size of the interval increases. C. As the level of confidence decreases, the size of the interval decreases.

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, $\mathrm{s}$, is found to be 10.

Step 2 ：Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, $E$ ?

Step 3 ：The margin of error, E, is calculated using the formula E = Z * (s/√n), where Z is the Z-score corresponding to the desired level of confidence, s is the sample standard deviation, and n is the sample size.

Step 4 ：As the level of confidence decreases, the Z-score decreases. Since the Z-score is a multiplier in the formula for E, a decrease in the Z-score will result in a decrease in E.

Step 5 ：Therefore, as the level of confidence decreases, the size of the interval decreases.

Step 6 ：\(\boxed{\text{Final Answer: The correct answer is C. As the level of confidence decreases, the size of the interval decreases.}}\)