Question

Question: A survey was conducted to attempt to determine how many hours the typical worker works during one year in the US. A survey of 33 workers found the mean number of hours worked in a year to be 1784 hours with a standard deviation of 65 hours.

a. Predict the actual mean number of hours worked by a worker in the US. State your answer using appropiate statistical terminology.

b. Explain what this answer means to someone who has never taken statistics, that is avoid statistical jargon and use common language. Use complete sentences.

*note: please give a step by step explanation for explaining what you did and why

Answer 1

Part a

We know that the sample mean is the unbiased estimator of the population mean. For prediction of actual mean we always use the random sample survey techniques. Based on the survey, we use the sample mean for the prediction of the population mean.

For this scenario, the sample mean is given as 1784 hours with the standard deviation of 65 years. Sample size is given as 33. So, actual mean number of hours worked by a worker in the US is predicted as 1784 hours.

Expected population mean = µ̅ = Xbar = 1784 hours

Part b

We have to find the average number of hours work by a worker in a year. We know that there are thousands of workers are working in the different industries. We cannot ask everyone about the number of hours work by them in a year. We cannot collect information for all workers regarding number of hours they worked in a year. So avoiding this fact, we can only collect the information of some employees and then based on this information we can find the average number of hours work by workers in US. What we will get from the collected information, we will assume this for entire workers in the US.