### Comparing the Effectiveness of Three Treatments Using a Randomized Block Design#### Background InformationIn this exercise, we aim to compare the effectiveness of three different treatments, labeled A, B, and C, using a randomized block design. A Friedman \( F_r \)-test is used to analyze the data collected. The data are organized into five blocks, as shown below:| Block | Treatment A | Treatment B | Treatment C ||-------|-------------|-------------|-------------|| 1 | 14 | 13 | 14 || 2 | 11 | 13 | 12 || 3 | 10 | 10 | 19 || 4 | 9 | 13 | 18 || 5 | 14 | 14 | 15 |#### Steps to Conduct the Friedman \( F_r \)-test**a. Specify the null and alternative hypotheses:**- **Null Hypothesis (\(H_0\))**: All of the probability distributions for the 3 treatments are identical.- **Alternative Hypothesis (\(H_a\))**: At least two of the probability distributions for the 3 treatments are different.**b. Specify the rejection region for the test:**- Use a significance level (\(\alpha\)) of 0.05.- The critical value from the Friedman test distribution is 5.991.- The rejection region for the test is \( F_r > 5.991 \) (rounded to three decimal places as needed).**c. Conduct the test and interpret the results:**- Calculate the test statistic \( F_r \) using the given data.- Formula: \[ F_r = \text{(Round to two decimal places as needed.)} \]Complete the calculation based on the specific steps required to compute the Friedman test statistic.Ensure to compare the computed \( F_r \) value with the critical value 5.991 to draw conclusions. If \( F_r > 5.991 \), reject the null hypothesis in favor of the alternative hypothesis.

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Description: ### Comparing the Effectiveness of Three Treatments Using a Randomized Block Design#### Background InformationIn this exercise, we aim to compare the effectiveness of three different treatments, labeled A, B, and C, using a randomized block design.

Introduction: There are three treatments, A, B, and C, which are to be compared in terms of…

Math

Statistics

Suppose you have used a randomized block design to help you compare the effectiveness of three different treatments, A, B, and C. You obtained the data given in the table to the right and plan to conduct a Friedman F,-test. Complete parts a through c below. Treatment Block A В 1 14 13 14 2 11 13 10 10 19 9. 13 18 14 14 15 a. Specify the null and alternative hypotheses you will test. Ho: All of the probability distributions for the 3 treatments is/are identical Ha: At least two of the probability distributions for the 3 treatments is/are different b. Specify the rejection region for the test. Use a = 0.05. F, 5.991 (Round to three decimal places as needed.) > c. Conduct the test and interpret the results. Find the test statistic F,. F, = (Round to two decimal places as needed.) O + N O O 5 N 3 4 5

Suppose you have used a randomized block design to help you compare the effectiveness of three different treatments, A, B, and C. You obtained the data given in the table to the right and plan to conduct a Friedman F,-test. Complete parts a through c below. Treatment Block A В 1 14 13 14 2 11 13 10 10 19 9. 13 18 14 14 15 a. Specify the null and alternative hypotheses you will test. Ho: All of the probability distributions for the 3 treatments is/are identical Ha: At least two of the probability distributions for the 3 treatments is/are different b. Specify the rejection region for the test. Use a = 0.05. F, 5.991 (Round to three decimal places as needed.) > c. Conduct the test and interpret the results. Find the test statistic F,. F, = (Round to two decimal places as needed.) O + N O O 5 N 3 4 5

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 6E: List the sample space of each experiment. Tossing three coins

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