Q.1 - The Practice of Statistics for AP

Question

Conditions Martin says that the relative importance of the three conditions for performing inference is, in order from most to least important, Independent, Normal, and Random. Write a brief note to Martin explaining why he is incorrect. 

Step-by-Step Solution

Answer

The main conditions to perform independence:

• Data must be random.
• Values must be independent of each other.
• Data must be normally distributed.

Step 1: Given Information

Three conditions are most to least important.

Step 2: Explanation

Following are the main conditions to perform independence:

a. Data must be random.

b. Values must be independent of each other.

c. Data must be normally distributed.

All of the above-mentioned conditions are important due to the following reasons:

(a). Randomness is important for the representation of the entire true population. Without randomization conditions, it is not possible to perform inferences.

(b). Normality is the second condition that is must to perform inference because a large sample size (that is above $30$ ) is the representation of the population.

(c) The condition that is not important is the condition of independence because the independence could be assumed even if the size of the sample is below the $10\%$ of the size of the population