Textbook Question
Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:
a. Differences d
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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
1:39 minutesProblem 13.3.2f
Textbook Question
Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:
f. The critical value of T (assuming a 0.05 significance level in a test of no difference between hospital admissions of Friday 6th and the following Friday 13th).
Verified step by step guidance1
Identify the null hypothesis (H₀) and the alternative hypothesis (H₁). For the Wilcoxon signed-ranks test, the null hypothesis states that there is no difference between the two paired groups (hospital admissions on Friday 6th and Friday 13th). The alternative hypothesis states that there is a difference.
Determine the significance level (α). In this case, the significance level is given as 0.05.
Calculate the sample size (n). Count the number of non-zero differences between the paired data points. Exclude any pairs where the difference is zero, as these do not contribute to the test statistic.
Use the sample size (n) to find the critical value of T from the Wilcoxon signed-ranks test critical value table. Ensure you are using the correct table for a two-tailed test at the 0.05 significance level.
Compare the calculated test statistic (T) from the data to the critical value of T. If the test statistic is less than or equal to the critical value, reject the null hypothesis; otherwise, fail to reject the null hypothesis.
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Wilcoxon Signed-Ranks Test
The Wilcoxon signed-ranks test is a non-parametric statistical test used to compare two related samples or matched pairs. It assesses whether their population mean ranks differ, making it suitable for data that do not meet the assumptions of normality required for parametric tests. This test is particularly useful in situations where the sample size is small or when the data are ordinal.
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Step 2: Calculate Test Statistic
Critical Value
The critical value in hypothesis testing is a threshold that determines whether to reject the null hypothesis. It is derived from the chosen significance level (alpha), which indicates the probability of making a Type I error. For the Wilcoxon signed-ranks test, the critical value of T is compared against the calculated test statistic to decide if the observed differences in hospital admissions are statistically significant.
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Significance Level (α)
The significance level, often denoted as alpha (α), is the probability of rejecting the null hypothesis when it is actually true. A common choice for α is 0.05, which implies a 5% risk of concluding that a difference exists when there is none. In the context of the Wilcoxon signed-ranks test, this level helps determine the critical value and guides the interpretation of the test results.
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