Understanding the statistical scenario using R with basic concepts I am new to statistics, trying to solve below problem,
Two companies selling toothpastes with the lable of 100 grams per tube on the package. We randomly bought eight toothpastes from each company A and B from random stores. Afterwards, we scaled them using high precision scale. Our measurements are recorded as follows:
Company A: 97.1   101.3   107.8   101.9   97.4    104.5   99.5    95.1
Company B: 103.5  105.3   106.5   107.9   102.1   105.6   109.8   97.2

Is this a paired or unpaired experiment?
I am selecting it as paired.
Which nonparametric test statistic would you use to compare the medians of Company A and Company B.
I am selecting wilcoxon signed rank test
Use a nonparametric test statistic to check if there is a statistically significant difference between the medians of Company A and Company B.
article1 = c(97.1  , 101.3  , 107.8  , 101.9  , 97.4   , 104.5  , 99.5   , 95.1)
article2 = c(103.5 , 105.3  , 106.5  , 107.9  , 102.1  , 105.6  , 109.8  , 97.2)
wilcox.test(article1, article2, paired = 0)

Will you accept or reject your Null Hypothesis? ($\alpha = 0.05$) Are packaging process similar or different based on weight measurements? Why?
I am not understanding the last part Are packaging process similar or different based on weight measurements?, how I can process that part ?
Did I select the right function of R wilcox.test for Wilcoxon signed test?
 A: I see no reason to take these as paired data, from your descriptions of
the sampling. Why should the first tube from A be particularly related to the first tube from B?
x1=c(97.1, 101.3, 107.8, 101.9, 97.4, 104.5, 99.5, 95.1)
x2=c(103.5, 105.3, 106.5, 107.9, 102.1, 105.6, 109.8, 97.2)

Boxplots show different medians, perhaps significantly different at the 5% level.
median(x1); median(x2)
[1] 100.4
[1] 105.45

boxplot(x1, x2, col="skyblue2", horizontal=T)


A two-sample nonparametric Wilcoxon rank sum test shows P-value just barely below 5%, and so there is borderline significance. The boxplots show distributions of similar shape, so it is reasonable to interpret this
result as borderline significance between the two sample medians. You might say there is weak evidence that the packaging processes of A and B are different.
wilcox.test(x1, x2)

        Wilcoxon rank sum test

data:  x1 and x2
W = 13, p-value = 0.04988
alternative hypothesis: 
  true location shift is not equal to 0

I can see nothing wrong with doing the Wilcoxon Rank Sum test.
However, both samples give reasonably linear normal probability plots (Q-Q plots) and Shapiro-Wilk tests do not reject the null hypothesis of normality.
shapiro.test(x1)

        Shapiro-Wilk normality test

data:  x1
W = 0.96714, p-value = 0.8747

shapiro.test(x2)

        Shapiro-Wilk normality test

data:  x2
W = 0.9516, p-value = 0.7273

par(mfrow=c(1,2))
 qqnorm(x1);  qqline(x1, col="blue")
 qqnorm(x2);  qqline(x2, col="blue")
par(mfrow=c(1,1))


Thus, one could also look to see if A and B population means differ
using a Welch 2-sample t-test; it also shows a P-value very near 5%
(this time just barely above). Formally, you could reject the null
hypothesis that the population means are the same at the 6% level.
t.test(x1, x2)

        Welch Two Sample t-test

data:  x1 and x2
t = -2.0617, df = 13.913, p-value = 0.05844
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -8.4953497  0.1703497
sample estimates:
mean of x mean of y 
 100.5750  104.7375 

