A textile manufacturer wanted to know if the breaking load(kg/25 mm width) is greater for unabraded fabrics versus fabricsthat were abraded. Abraded fabrics are produced by the use offriction to produce surface wear on the fabric. The manufacturerrandomly selected equal-sized sections of 21 of their fabrics. Eachsection was then equally divided into two pieces, with the abrasionprocess being applied to one of them. The tensile strengthmeasurements were taken for all of the fabric pieces with theresults given in the following table. You will not need to use theinformation from all the rows. Please assume that the distributionis normal.

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

Please explain the correct answer. If this is a pairedsituation, please state the common characteristic that makes thesedata 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 tensilestrength of the unabraded fabrics is greater than the mean strengthof the abraded fabrics? Use α = 0.05.

Using R studio code, calculate the test statistic. Be sure thatthe 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 thissituation.

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

Interpret the interval or bound calculated above.

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

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