Use the Wilcoxon rank sum test on the following data to...

Use the Wilcoxon rank sum test on the following data to determine whether the two population locations differ. (Use a $10 \%$ significance level.) $$ \begin{array}{rrrrrrrrrrr} \hline \text { Sample 1: } & 15 & 7 & 22 & 20 & 32 & 18 & 26 & 17 & 23 & 30 \\ \text { Sample 2: } & 8 & 27 & 17 & 25 & 20 & 16 & 21 & 17 & 10 & 18 \\ \hline \end{array} $$

Use the Wilcoxon rank sum test on the following data to determine whether the two population locations differ. (Use a $10 \%$ significance level.)
$$
\begin{array}{rrrrrrrrrrr}
\hline \text { Sample 1: } & 15 & 7 & 22 & 20 & 32 & 18 & 26 & 17 & 23 & 30 \\
\text { Sample 2: } & 8 & 27 & 17 & 25 & 20 & 16 & 21 & 17 & 10 & 18 \\
\hline
\end{array}
$$

Key Concepts

Hypothesis Testing

Hypothesis testing involves formulating a null hypothesis, which typically states that there is no difference between the groups, and an alternative hypothesis that claims a difference exists. The test then uses calculated statistics and probability thresholds, such as the significance level, to decide whether to reject the null hypothesis.

Wilcoxon Rank Sum Test

The Wilcoxon rank sum test is a nonparametric statistical test used to compare two independent samples to assess whether their population distributions differ, particularly in terms of their central tendency (medians). It is often used as an alternative to the two-sample t-test when the assumptions of normality or equal variances are not met.

Significance Level

A significance level is the threshold used in hypothesis testing to determine whether a test result is statistically significant. In this context, a 10% significance level indicates that there is a 10% risk of rejecting the null hypothesis when it is actually true, helping to balance the risks of Type I and II errors.

Ranking Procedure

The ranking procedure is a critical part of the Wilcoxon rank sum test. It involves sorting all observations from both samples together and assigning ranks to the values. The sums of the ranks for each sample are then used in further computations to determine if there is a statistically significant difference between the samples.

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