In a Wilcoxon signed rank test, the test statistic is calculated as 20. If there are n = 10 observations for which Ha: D > 0, and a test is performed at the 5% significance level, then what is the result?

 In a Wilcoxon signed rank test, the test statistic is calculated as 20. If there are n = 10 observations for which Ha: D > 0, and a test is performed at the 5% significance level, then what is the result?👇🏾👇

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In a Wilcoxon signed rank test, we need to compare the test statistic to the critical value at the given significance level to determine whether to reject the null hypothesis. Here's a step-by-step process to determine the result:

1. Hypotheses:

   • ${𝐻}_0:$ The median difference $𝐷=0$
   • ${𝐻}_{𝑎}:$ The median difference $𝐷>0$

2. Given:

   • Sample size $𝑛=10$
   • Test statistic $𝑇=20$
   • Significance level $𝛼=0.05$

3. Critical value: For $𝑛=10$, we need to find the critical value from the Wilcoxon signed rank test table for a one-tailed test at the 5% significance level.

   The critical value for $𝑛=10$ at $𝛼=0.05$ (one-tailed test) is ${𝑊}_{0.05,10}=8$.

4. Decision rule:

   • Reject ${𝐻}_0$ if the test statistic $𝑇\le$ critical value.
   • Do not reject ${𝐻}_0$ if $𝑇>$ critical value.

5. Comparison:

   • The test statistic $𝑇=20$
   • The critical value ${𝑊}_{0.05,10}=8$

Since $𝑇=20$ is greater than the critical value of 8, we do not reject the null hypothesis ${𝐻}_0$.

Result: At the 5% significance level, there is not enough evidence to reject the null hypothesis. Thus, we do not conclude that the median difference $𝐷$ is greater than 0.