Understanding Sampling and Mean Estimation

A company manager conducted a survey to estimate employees' travel time by sampling the first 20 arrivals each day for three weeks. The sample means were compared to the true mean travel time of 25 minutes, revealing a discrepancy. The video discusses the lack of randomness in the sampling method and evaluates whether the sample means are representative of the entire employee population.

What was the manager's primary goal in the task described?

• To find the fastest route to work

• To estimate the mean travel time for employees

• To reduce travel time for employees

• To increase employee productivity

How did the manager collect data on employee travel times?

• By asking employees to fill out a survey

• By observing employees' arrival times

• By using GPS tracking on employee vehicles

• By surveying the first 20 employees to arrive each day

What was the manager's method for calculating the sample mean?

• Adding all times and dividing by 10

• Using the mode of all times

• Using the median of all times

• Adding all times and dividing by the number of employees

How often did the manager repeat the data collection process?

• Every month

• Twice a week

• Every day for 3 weeks

• Once a week

What was the true mean travel time for the entire employee population?

• 20 minutes

• 15 minutes

• 25 minutes

• 30 minutes

What does the sample mean represent in this context?

• The slowest travel time recorded

• The average travel time for the first 20 employees each day

• The average travel time for all employees

• The fastest travel time recorded

Why was the manager's sampling method not considered random?

• It only surveyed the first 20 employees to arrive

• It used a lottery system

• It only surveyed employees who arrived late

• It included all employees

What factor might affect the travel time of the first 20 employees?

• All of the above

• The time they leave home

• Their mode of transportation

• The amount of traffic they encounter

What impact did the sampling method have on the representativeness of the sample mean?

• It had no impact on the sample mean

• It made the sample mean lower than the true mean

• It made the sample mean higher than the true mean

• It made the sample mean equal to the true mean

What conclusion can be drawn about the sample means?

• They accurately represent the entire population

• They are higher than the true mean

• They are equal to the true mean

• They are not representative of the entire population