Average Wasted Time Per Day Analysis
How can we analyze the average wasted time per day among employees?
Suppose a CEO wants to determine if the employees in her company waste less time than the 120 minutes reported in an article. A random sample of 10 employees provided the following data: 127, 175, 131, 134, 125, 107, 91, 136, 47. How can we calculate the average wasted time per day and estimate the population mean with 95% confidence?
Analysis of Average Wasted Time Per Day
Based on the provided sample data, the average amount of time wasted every day is 119.3 minutes. With 95% confidence, the population mean can be estimated with a margin of error of about 33.68 minutes.
The CEO polls ten randomly selected employees on their wasted time to determine if the average daily wasted time is less than the 120 minutes mentioned in the article. The sample data consists of the following numbers: 127, 175, 131, 134, 125, 107, 91, 136, and 47.
(a) To calculate the sample mean, we sum up the values and divide by the sample size of 10: mean = (127 + 175 + 131 + 134 + 125 + 107 + 91 + 136 + 47) / 10 = 119.3 minutes.
(b) To estimate the population mean with a 95% confidence level, we can calculate the margin of error using the formula: margin of error = critical value * (standard deviation / √n). Given the known population standard deviation of 54, and using the critical value of 1.96 for a 95% confidence level, the margin of error is approximately 33.68 minutes.
By analyzing the data, we can conclude that the average wasted time per day among employees is 119.3 minutes, with a margin of error of 33.68 minutes for the population mean estimation.