Question

One large course has 900 students, broken down into section meetings with 30 students each. The section meetings are led by TA's. On the final, the class avg is 63 and the SD is 20. However, in one section the avg. is only 55. The TA argues this way:If you took 30 students at random from the class, there is a good chance they would avg below 55 on the final. Chance variation.Is this a good argument? Yes or no, explain.

Answer 1

Answer:

The argument made by the TA is not good.

Step-by-step explanation:

The argument made by the TA is that in a random sample of 30 students there is a good chance that the class average would be below 55.

As the sample size is large (n ≥ 30), the sampling distribution of sample mean will follow a Normal distribution.

The mean and standard deviation of this sampling distribution are:

$\mu_{\bar x}=\mu\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

The information provided is:

$\mu=63\\\sigma=20\\n=30$

Compute the probability that sample mean is less than 55 as follows:

$P(\bar X<55)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{55-63}{20/\sqrt{30}} )\\=P(Z<-2.19)=1-P(Z<2.19)\\=1-0.9857\\=0.0143$

The probability that a random sample of 30 students have a class average below 55 is 0.0143.

The probability is very small.

The event of 30 student having an average below 55 is an unusual event.

Unusual events are those events that have a very low probability of occurrence.

Thus, the argument made by the TA is not good.