Wilcoxon Sign Rank Test rejection region

In summary, the conversation discusses a study comparing two computer software packages for use in inventory control. The null hypothesis is that the packages are identical, while the alternative hypothesis is that they are not the same. The results of the study show that the packages are not equally rapid in handling computing tasks, and it is concluded that package x is faster than package y. The use of α = 0.05 for a two-tailed test is questioned, but it is determined that the table for the Wilcoxon signed rank test should already account for this.
  • #1
tzx9633

Homework Statement


Two computer software packages are being considered for use in the inventory control department of a small manufacturing firm. The firm has selected 12 different computing task that are typical of the kinds of jobs. The results are shown in the table below. At the 0.05 level, can we conclude that those two computer software packages are identical?

1.Ho: those two computer software packages are identical
H1: those two computer software packages are not same
2. Based on the alternative hypothesis, the test is min (〖 T〗^+, 〖 T〗^-) = min(8.5, 57.5) = 8.5
3.α = 0.05, n = 12 – 1 = 11

. From table of Wilcoxon signed rank for two tail test,

α = 0.05, n = 11, then a = 14
We will reject Ho if min (〖 T〗^+, 〖 T〗^-) ≤ a
5. Since min(8.5, 57.5) = 8.5 ≤ 14, thus we reject Ho and conclude that the software packages are not equally rapid in handling computing tasks like those in the sample, or the population median for 〖di=x〗_i-y_i is not equal to zero and that package x is faster than package y in handling computing task like ones sample.

Homework Equations

The Attempt at a Solution



In this question , we already knew that it's 2 tailed test , why the author still use α = 0.05 , not α/2 = 0.025 ? I think it's wrong ... [/B]
I think we should use α/2 = 0.025 when finding the U critical
 

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  • #2
If you are using a table for the Wilcoxon signed rank for two tail test you should not have to make any adjustments of the α value. The table should already have adjusted for that.
 

1. What is the Wilcoxon Sign Rank Test rejection region?

The Wilcoxon Sign Rank Test rejection region is a critical region that is used to determine whether the null hypothesis should be rejected or not. It is a range of values that, if the test statistic falls within it, would lead to the rejection of the null hypothesis.

2. How is the Wilcoxon Sign Rank Test rejection region calculated?

The Wilcoxon Sign Rank Test rejection region is calculated by first determining the significance level (alpha) and the sample size (n). Then, using a table or statistical software, the critical values for the test statistic are found and the rejection region is defined based on these values.

3. Why is the Wilcoxon Sign Rank Test rejection region important?

The Wilcoxon Sign Rank Test rejection region is important because it helps to determine whether the results of the test are statistically significant or not. If the test statistic falls within the rejection region, it means that the null hypothesis can be rejected and the alternative hypothesis can be accepted.

4. What are some common misconceptions about the Wilcoxon Sign Rank Test rejection region?

One common misconception about the Wilcoxon Sign Rank Test rejection region is that it is the same as the p-value. While both are used to determine the statistical significance of the results, the rejection region is based on the critical values of the test statistic, while the p-value is a probability value that represents the likelihood of obtaining the observed results if the null hypothesis is true.

5. How can the Wilcoxon Sign Rank Test rejection region be interpreted?

The Wilcoxon Sign Rank Test rejection region can be interpreted as the range of values for the test statistic that are considered too extreme to be explained by chance alone. If the test statistic falls within this region, it suggests that the null hypothesis is not true and the alternative hypothesis should be accepted. However, if the test statistic falls outside of the rejection region, it means that the results can be explained by chance and the null hypothesis should be accepted.

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