Question

A textile manufacturer wanted to know if the breaking load (kg/25 mm width) is greater for unabraded fabrics versus fabrics that were abraded. Abraded fabrics are produced by the use of friction to produce surface wear on the fabric. The manufacturer randomly selected equal-sized sections of 21 of their fabrics. Each section was then equally divided into two pieces, with the abrasion process being applied to one of them. The tensile strength measurements were taken for all of the fabric pieces with the results given in the following table. You will not need to use the information from all the rows. Please assume that the distribution is normal.

a) Should this situation be analyzed via a two-sample independent or paired method?

Please explain the correct answer. If this is a paired situation, please state the common characteristic that makes these data paired.

b) What is the alternative hypothesis for this situation?

Please explain the correct answer.

c) Is there any evidence to suggest that the mean tensile strength of the unabraded fabrics is greater than the mean strength of the abraded fabrics? Use α = 0.05.

Using R studio code, calculate the test statistic. Be sure that the information for the unabraided fabric is first.

Using R studio code, calculate the p-value.

Write the complete four steps of the hypothesis test for this situation.

d) Calculate the appropriate confidence interval or bound for the mean based on the question in part c). If you calculate a bound, type 10000 to indicate ∞.

Interpret the interval or bound calculated above.

e) In practical terms, does the data imply that the mean tensile strength of the unabraded fabrics is greater than that of the abraded fabrics? Please explain your reasoning. This part uses the information from parts c) and d)

f) Explain why the results in parts c) and d) are consistent with each other.

Answer 1