Question

In a Blowroom, a study was made to compare the fibre fracture using 2 Bladed and Kirschner beater. When the same mixing was processed using two Blowroom lines, the best statistical measure to choose is

• A. t-Test
• B. F-test
• C. Chi-square Test
• D. Kruskal--Wallis Test

Hint:

Remember the applications of common statistical tests: \[ \begin{array}{|c|c|} \hline \textbf{Statistical Test} & \textbf{Application} \hline t\text{-Test} & \text{Compare Means of Two Groups} \hline F\text{-Test} & \text{Compare Variances} \hline Chi\text{-square Test} & \text{Categorical/Frequency Data} \hline Kruskal--Wallis Test & \text{Compare Three or More Groups} \hline \end{array} \] A useful memory trick is: \[ \boxed{ 2\ \text{Groups} \Longrightarrow \text{t-Test} } \] \[ \boxed{ 3\ \text{or More Groups} \Longrightarrow \text{Kruskal--Wallis Test} } \] Questions on selecting the appropriate statistical test are frequently asked in textile quality control and engineering statistics examinations.

Answer 1

The Correct Option is A

Concept: In textile engineering, statistical tests are frequently used to compare the performance of different machines, processes, or materials. The choice of the statistical test depends on the type of data and the objective of the study. The commonly used statistical tests are:
• t-Test: Used to compare the means of two independent groups.
• F-Test: Used to compare the variances of two populations.
• Chi-square Test: Used for categorical data and testing independence or goodness of fit.
• Kruskal--Wallis Test: A non-parametric test used for comparing three or more independent groups. Whenever only two groups are compared with respect to their average values, the Student's t-test is the most appropriate statistical tool.

Step 1: Identify the objective of the experiment.
The study compares fibre fracture produced by \[ \begin{aligned} &\bullet\ \text{2-Bladed Beater} &\bullet\ \text{Kirschner Beater} \end{aligned} \] Thus, there are only \[ \boxed{2\ \text{independent groups}.} \] The objective is to determine whether there is a significant difference in the average fibre fracture produced by the two beaters.

Step 2: Select the appropriate statistical test.
Since the comparison involves the means of only two independent samples, \[ \boxed{ \text{Student's t-Test} } \] is the most suitable statistical method. The t-test determines whether the observed difference between the sample means is statistically significant.

Step 3: Examine each option.
Option (A): t-Test Used to compare the means of two independent groups. \[ \boxed{\text{Correct}} \] Option (B): F-Test Primarily used to compare population variances rather than sample means. \[ \boxed{\text{Incorrect}} \] Option (C): Chi-square Test Applicable to categorical or frequency data, not continuous fibre fracture measurements. \[ \boxed{\text{Incorrect}} \] Option (D): Kruskal--Wallis Test Used when comparing three or more independent groups under non-parametric conditions. Since only two groups are involved, this test is unnecessary. \[ \boxed{\text{Incorrect}} \]

Step 4: Write the final answer.
Since the experiment compares the mean fibre fracture of two independent Blowroom lines, \[ \boxed{ \text{Student's t-Test} } \] is the most appropriate statistical measure. Therefore, \[ \boxed{\text{Option (A) is the correct answer.}} \]