Question

At the local college, a study found that students completed an average of 3.5 classes per semester. A sample of 49 students was taken. What is the best point estimate for the average number of classes per semester for all students at the local college?

Answer 1

By the Central Limit Theorem, the best point estimate for the average number of classes per semester for all students at the local college is 3.5.

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.

The mean of the sample is 3.5 classes per semester.

By the Central Limit Theorem, the best point estimate for the average number of classes per semester for all students at the local college is 3.5.