An economist is interested in studying the incomes of consumers in a particular region.The population standard deviation is known to be $2,000.A random sample of 50 individuals resulted in an average income of $30,000.
-What is the width of the 90% confidence interval?
A) $930.56
B) $1,457.20
C) $465.20
D) $728.60

Question

Quizplus · Accepted Answer

The width of the confidence interval can be calculated using the formula for the margin of error: $Z \times \frac{\sigma}{\sqrt{n}}$, where $Z$ is the Z-score corresponding to the desired confidence level (for 90%, $Z = 1.645$), $\sigma$ is the population standard deviation ($2,000), and $n$ is the sample size (50). The width of the confidence interval is twice the margin of error. Thus, the calculation is $2 \times 1.645 \times \frac{2000}{\sqrt{50}} \approx 930.56$.

An Economist Is Interested in Studying the Incomes of Consumers