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there is a question like this: Two producers produce a cream with hydrating ingredient. According to the table state, whether the amount of the ingredient is significantly different or not. Use the level of significance 0.05 and assume that data are not from a normal distribution.

1st producer samples {1,52 ,1,57 ,1,71 ,1,34 ,1,68}

2nd producer samples {1,75 ,1,67 ,1,56 ,1,66 ,1,72 ,1,79 ,1,64 1,55}

I know I have to solve it in with a non-parametric test, can I use Man-Whitney U test? or you suggest something else for this?

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Mann-Whitney U test (also called Wilcoxon signed-rank test) seems appropriate for testing your null hypothesis if the data cannot be assumed to be normal.

Here are results for R statistical software: No significant difference.

x1 = c(1.52, 1.57, 1.71, 1.34, 1.68)
x2 = c(1.75, 1.67, 1.56, 1.66, 1.72, 1.79, 1.64, 1.55)
wilcox.test(x1, x2)

        Wilcoxon rank sum test

data:  x1 and x2
W = 12, p-value = 0.2844
alternative hypothesis: 
  true location shift is not equal to 0
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