Question

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

Answer 1

Answer:

The true mean $\mu$ it probably could be larger, smaller, or equal to 22

Step-by-step explanation:

False.

By definition the sample mean is defined as:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

For this case the value for the sample size is n =190 and the calculated sample mean is $\bar X=22$. This value represent the sample and for this case we can't assume that this value represent at all the population as the population mean $\mu$ since we probably have variability from the data of the students at City College.

So we can conclude that the true mean $\mu$ it probably could be larger, smaller, or equal to 22

Answer 2

Answer: could be larger, smaller or equal to 22

Step-by-step explanation:

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College could be larger, smaller or equal to 22( which is the sample mean).

In most cases the sample mean are not always equal to the population mean. The sample used might have been taken randomly, but might still contain more of the larger value or smaller values of the population leading to deriving a different sample mean entirely from the population mean.

Therefore, for this case the sample is the 190 students selected for the analysis while the population is the total number of students in the city, so the population mean might either be larger, smaller or equal to the samples mean depending on the samples selected for the research.