Question

a job candidate with an offer from a prominent investment bank wanted to estimate how many hours she would have to work per week during her first year at the bank. she took a sample of six first-year analysts, asking how many hours they worked in the last week. a. construct a 95% confidence interval with her results: 64, 82, 74, 73, 78, and 87 hours. b. what will happen to the width of the confidence interval for the average hours of work if the job candidate uses a smaller confidence level than 95%? explain.

Answer 1

To construct the 95% confidence interval for the average work hours, calculate the sample mean and standard deviation, find the t-score for 95% confidence, and calculate the margin of error to apply to the mean. A smaller confidence level than 95% would result in a narrower confidence interval.

Step-by-step explanation:

To construct a 95% confidence interval for the average work hours of a first-year analyst at an investment bank using the sample hours provided (64, 82, 74, 73, 78, and 87), we will follow these steps:

1. Calculate the sample mean (mean) and sample standard deviation (standard deviation).
2. Since the sample size is small (n < 30) and we do not know the population standard deviation, we will use the t-distribution to find the t-score corresponding to a 95% confidence level.
3. Use the t-score and sample standard deviation to calculate the margin of error (margin of error).
4. Apply the margin of error to the sample mean to find the upper and lower bounds of the confidence interval.

Regarding part b, if we decrease the confidence level from 95% to a smaller percentage, the width of the confidence interval would decrease because we are allowing for more uncertainty. A smaller confidence interval implies less confidence that the interval contains the true population mean.