"Kiosks Yolanda opened a new fast food restaurant. From her first customer, Yolanda kept track of the time a patron needed to wait from the time placing the order to the time the customer received his/her order. Because she was unhappy with the wait time, she invested in Kiosks to take orders with the goal of decreasing wait times. In a random sample of 20 customers, it was found the wait time was 52.3 seconds.
b. Determine the mean wait time of the 10,303 customers."

Verified step by step guidance

1. Step 1: Understand the problem context. The problem states that a sample of 20 customers had an average wait time of 52.3 seconds. This is a sample mean, not the population mean.
2. Step 2: Identify what is being asked. The question asks to determine the mean wait time of the 10,303 customers, which is the population mean based on the sample data.
3. Step 3: Recognize that the sample mean is the best point estimate for the population mean when no other information is given. Therefore, the mean wait time for the 10,303 customers can be estimated by the sample mean of 52.3 seconds.
4. Step 4: If you want to be more precise, consider constructing a confidence interval around the sample mean to estimate the population mean with a certain level of confidence. This would require the sample standard deviation or variance, which is not provided here.
5. Step 5: Conclude that without additional data, the best estimate for the mean wait time of all 10,303 customers is the sample mean of 52.3 seconds.

Key Concepts

Sample Mean vs. Population Mean

The sample mean is the average calculated from a subset of data, while the population mean is the average of the entire group. In this question, the 52.3 seconds is the sample mean from 20 customers, but the mean wait time for all 10,303 customers (population mean) may differ and often requires additional data or assumptions to estimate.

Inference from Sample to Population

Statistical inference involves using sample data to make estimates or test hypotheses about a population. To determine the mean wait time of all customers, one typically uses the sample mean as an estimate, but must consider variability and confidence intervals to understand the accuracy of this estimate.

Random Sampling

Random sampling ensures that every individual in the population has an equal chance of being selected, which helps produce unbiased and representative data. The question mentions a random sample of 20 customers, which is crucial for making valid inferences about the entire customer population.