Question

1. Give a Real-life example of inferential statistics that will clearly identify your target population; how you would plan on acquiring a random representative sample; and then how you would use this sample to make inferences regarding your target population using this sample.

2. Give an example of a Discrete Variable and an example of a Continuous Variable. Can you also provide your reasoning by Answer the following questions:

Can your variable only be described using whole numbers? If so, it is a numerical discrete variable.

Can your variable only be described using the real number line? In other words, it falls on a continuum. If so, it is a numerical continuous variable.

Answer 1

(1)

Example - A coaching institute claiming that the average GPA of a student studying in there institute is 4.0.

In this case, the target population is all the students studying in that institute. We can just randomly select n number of students from N students in the institute to find a sample for our analysis.

We then set up our null and alternative hypothesis and then compute the mean GPA for these n students and apply a suitable parametric test based on the assumptions and conditions. If the test statistic falls in the critical region, we reject the null hypothesis.

(2)

Discrete Variable - Number of siblings a person has.

It will always be the whole number as the number of siblings of any person can never be in fractions or decimals. Therefore, if the variables can be only described using the whole number, then it is numerical discrete number.

Continuous Variable - Height of students in a class.

The height of the students are often collected in decimals, that is, it lies within a range and can have infinite values within that range. Therefore, we can say that if the variable can be described using the real number line, then is a numerical continuous variable.