An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the upper end point in a 99% confidence interval for the average income?
A) $15,141
B) $15,364
C) $15,052
D) $15,330

Question

Quizplus · Accepted Answer

We can use the formula: 
Upper end point = sample mean + margin of error

The margin of error for a 99% confidence interval can be found using the z-score table. The z-score corresponding to a 99% confidence level is 2.576.

Margin of Error = z-score * (population standard deviation / sqrt(sample size))
Margin of Error = 2.576 * (1000 / sqrt(50))
Margin of Error = 2.576 * 141.42
Margin of Error = 364.31

Upper end point = 15,000 + 364.31
Upper end point = $15,364

Therefore, the answer is B.

An Economist Is Interested in Studying the Incomes of Consumers