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Mathematics & Economics
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Research Paper
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English (U.S.)
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Topic:

Temperature and Fabric (Dye) Types on the Fabric Shrinkage Paper

Research Paper Instructions:

Research Paper A study of the effect of 4 temperature settings on percent shrinkage in dyeing fabrics was made on 4 replications for each of 3 types of fabric in a completely randomized design. The data are the percent shrinkage of three replicate fabric pieces dried at each of the 4 temperatures, and are in shrinks1.xls. Write a research paper to investigate the effect of temperature and fabric (dye) types on the fabric shrinkage. To complete your research paper, you need to (a) Construct side-by-side boxplots the means by temperature with separate “profiles” for each fabric. (b) Write out the individual linear models for fabric dye types and temperature, respectively, and obtain the analysis of variance for the data. (c) Fit the ANOVA model to test for a temperature effect at the alpha=0.05 significance level. Clearly state: null and alternative hypotheses, test statistic, rejection region and P-value. Include any computer output you obtain. Include a one-way ANOVA table if needed . (d) Test for a fabric (dye) effect at the alpha=0.05 significance level. Clearly state: null and alternative hypotheses, test statistic, rejection region and P-value. Include any computer output you obtain. Include a one-way ANOVA table if needed . (e) Check the following two assumptions under the test in (c) and (d). i. Does the evidence suggest that the data for each fabric (dye) group are not normal? Include the plots in a figure in your report. ii. Does the assumption of constant variance hold? Why or why not? Attach all R commands and R output used in an appendix. Label all necessary Figures and Tables and refer to these figures and tables from the text of your report.

Research Paper Sample Content Preview:

Temperature and Fabric (Dye) Types on the Fabric Shrinkage
Your Name
Department, University
Course number: Course name
Professor’s Name
Date
Temperature and Fabric (Dye) Types on the Fabric Shrinkage
* Side-by-Side Boxplots
Figure 1
Mean Shrinkage of Fabric by Temperature
Note. Temp1 = Red; Temp2 = Orange; Temp3 = Green; Temp4 = Blue. Each profile of the fabric is labeled as Dye1 (D1), Dye2 (D2), and Dye3 (D3).
In figure 1, the observed lowest percent shrinkage is recorded in temperature 1 dye 1 (D1.T1), while the highest percent shrinkage recorded is in temperature 4 dye 3 (D3.T4). Additionally, dye 1 is consistent to record the lowest percent shrinkage in each temperature while dye 3 is consistent to record the highest percent shrinkage in each temperature. The same is true with the median values of each dye profile where dye 1 is lowest while dye 3 is highest across different temperature settings.
* Linear Model and Two-Factor ANOVA
Figure 2
Normal Distribution between the Interaction of Dye and Temperature
Note. Quantile plots follow a straight line with slight deviation
Table 1
Shapiro-Wilk Test for Normality
W Value

P-value

0.9684

0.2194

In figure 2, the quantile plots of the percent shrinkage follow a straight diagonal line, which implies normal distribution in the data. However, there is a slight deviation along the line. In table 1, a Shapiro-Wilk test was used to determine the normality of the distribution. The p-value p= 0.2194 is greater than 0.05; therefore, the data is normally distributed.
Table 2
Two-Factor Analysis of Variance Table

df

Sum of Sq.

Mean Sq.

F Value

Pr(>F)

Dye

2

161.383

80.692

46.5623

1.036e-10 *

Temp

3

285.092

95.031

54.8363

1.673e-13 *

Interaction

6

14.440

2.407

1.3887

0.2457

Residual

36

62.387

1.733



*p < .05, two-tailed.
The probability values are p = 1.036e-10 (Dye), p =.1.673e-13 (Temperature), and p = 0.2457, ns (Interaction). In table 2, the p-values of the main factors dye and temperature are less than 0.05, but the p-value of the interaction is greater than 0.05. Therefore, there is a significant difference in the percent shrinkage among the three dye fabrics (F2,36 = 1.036e-10, p<.05). There is a significant difference in the percent shrinkage among the four temperature settings (F3,36 = 1.673e-13, p<.05). However, the interaction between dye and temperature has no significant difference in the percent shrinkage (F6,36 = 0.2457, p>.05).
* ANOVA Model for Temperature
Table 3
One-Way ANOVA Table for Temperature

df

Sum of Sq.

Mean Sq.

F Value

Pr(>F)

Temp

3

285.092

95.031

17.553

1.223e-07 *

Residual

44

238.21

5.414



*p < .05, two-tailed.
The null hypothesis for the temperature factor is that there is no significant difference in the percent shrinkage among the four temperature settings. On th...
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