Question

The mean GPA for 126 residents of the local apartment complex is 3.3.

Answer 1

Answer:

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 3.3

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of the sample:

126 students, mean of 3.3

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 3.3

Answer 2

Answer:

The sample mean is the best point estimate  of the population mean.

Step-by-step explanation:

Let's recall that:

1. For all populations, the sample mean is an unbiased  estimator of the population mean, meaning that the  distribution of sample means tends to center about  the value of the population mean.

2. For many populations, the distribution of sample  means x tends to be more consistent (with less  variation) than the distributions of other sample  statistics.

Therefore, we can conclude that the best point estimate of  the mean GPA for all residents of the local apartment complex is 3.3