Asked by Virgil Hobbs on Apr 27, 2024
Verified
The manager of a grocery store has taken a random sample of 144 customers.The average length of time it took these 144 customers to check out was 3 minutes.It is known that the standard deviation of the population of checkout times is 1 minute.With a .95 probability, the sample mean will provide a margin of error of
A) 1.63.
B) .137.
C) .163.
D) 1.37.
Margin of error
An expression of the amount of random sampling error in a survey's results. It represents the range within which the true value lies, based on a certain confidence level.
Sample mean
The average of a set of data points or observations taken from a larger population.
Checkout times
The duration or period it takes for a customer to complete a purchase transaction from start to finish.
- Implement suitable formulas to determine the standard error of the mean and the margin of error across diverse scenarios.
Verified Answer
Margin of error = z* (standard deviation / square root of sample size)
We are given that the standard deviation of the population is 1 minute, and the sample size is 144. We need to find the value of z for a 95% confidence level. This can be found using a standard normal distribution table or calculator, and we get:
z = 1.96
Plugging in the values, we get:
Margin of error = 1.96 * (1 / sqrt(144))
Margin of error = 1.96 * (1 / 12)
Margin of error = 0.163
Therefore, the correct answer is C: 0.163.
Learning Objectives
- Implement suitable formulas to determine the standard error of the mean and the margin of error across diverse scenarios.
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