Question

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

What is the best point estimate for the mean GPA for all residents of the local apartment complex?

Answer 1

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

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

Answer 2

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

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 = (\sigma)/(√(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