Question

Now imagine that administrators at this college are willing to divulge to you the standard deviation of incomes for all alumni from 10 years ago, and you learn that = $50,000. Repeat the confidence interval in part (b) using this new information, and make sure you use the procedure that considers this new information. (Enter your answer using interval notation. Express your answers in dollars and round your numerical values to one decimal place.)

a) $58,000 to $64,000
b) $55,000 to $61,000
c) $52,000 to $58,000
d) $50,000 to $56,000

Answer 1

To calculate the confidence interval for a known population standard deviation, the formula mean ± (Z-score * (standard deviation/sqrt(n))) is used, with the Z-score corresponding to the chosen confidence level.

Step-by-step explanation:

The question seeks to establish a confidence interval for the mean income of alumni using a known standard deviation. When we have the standard deviation of a population, we use the normal distribution (as opposed to the t-distribution used when the standard deviation is unknown) to calculate confidence intervals. In this case, the standard deviation is given as $50,000.

To calculate a confidence interval, we use the formula: mean ± (Z-score * (standard deviation/sqrt(n))), where the Z-score is determined based on the desired confidence level, and n is the sample size. Since the question does not specify the confidence level nor the sample size, we can't calculate the interval precisely; however, the answer would be structured around this formula, adjusting with the Z-score corresponding to the given confidence level and the actual sample size.