A sample of size n=50 is drawn from a population whose standard deviation is $\sigma = 14.5$ Find the margin of error for a 90 % confidence interval for $\mu .$
A) 3.37
B) 0.80
C) 0.89
D) 2.05

Question

A sample of size  n=50  is drawn from a population whose standard deviation is $\sigma = 14.5$ Find the margin of error for a  90 %  confidence interval for  $\mu .$
A)  3.37 
B)  0.80 
C)  0.89 
D)  2.05

Quizplus · Accepted Answer

The margin of error (ME) for a confidence interval can be calculated using the formula $ME = z \times \frac{\sigma}{\sqrt{n}}$, where $z$ is the z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. For a 90% confidence interval, the z-score is approximately 1.645. Plugging in the values: $ME = 1.645 \times \frac{14.5}{\sqrt{50}} \approx 3.37$.

A Sample of Size N=50 Is Drawn from a Population