Homework Problem 23 section 9.2

Kellie Stilson

1. Fusible interlinings are being used with increasing frequency to support outer fabrics and improve the shape and drape of various pieces of clothing. The article gave the accompanying data on extensibility (%) at 100 gm/cm for both high quality (H) and poor quality (P) fabric specimens.

H <- c(1.2, 0.9, 0.7, 1, 1.7, 1.7, 1.1, 0.9, 1.7, 1.9, 1.3, 2.1, 1.6, 1.8, 1.4, 
    1.3, 1.9, 1.6, 0.8, 2, 1.7, 1.6, 2.3, 2)
P <- c(1.6, 1.5, 1.1, 2.1, 1.5, 1.3, 1, 2.6)

a.) Construct normal probability plots to verify the plausibility of both samples having been selected from normal probability distributions.

qqnorm(H)
qqline(H)

qqnorm(P)
qqline(P)

Since both plots nearly follow the line, this is plausible.

b.) Construct a comparative boxplot. Does it suggest there is a difference between true average extensibility for H and P?

boxplot(H, P, names = c("High Quality", "Poor Quality"), col = c("skyblue", 
    "lightgreen"))

From the boxplot, there does not seem to be a drastic difference in the means of the two data sources, however, the H data is skewed low, and the P data is skewed high.

c.) Use the two-sample t-test to decide whether true average extensibility differs for the two types of fabric.

t.test(H, P, alternative = c("two.sided"))

## 
##  Welch Two Sample t-test
## 
## data:  H and P
## t = -0.3801, df = 10.48, p-value = 0.7115
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.5404  0.3820
## sample estimates:
## mean of x mean of y 
##     1.508     1.588

Since our p value is 0.7115 and is much greater than 0.1, then we cannot reject the null hypothesis and statistically conclude that the true average extensibility does not differ for the two types of fabric.