Explanation Calculation: From the given information the value of α is 0.01, and to test the claim that the distributions of growths are different for root stocks A and B . The null and alternative hypothesis is, Null hypothesis: H 0 : The distributions of growths are same for root stocks A and B . Alternative hypothesis: H 1 : The distributions of growths are different for root stocks A and B . Test statistic : The z value for the sample test statistic R is, z = R − μ R σ R In the formula R is the sum of ranks from the sample of size n 1 (smaller sample), μ R = n 1 ( n 1 + n 2 + 1 ) 2 σ R = n 1 n 2 ( n 1 + n 2 + 1 ) 12 n 1 be the sample size of the smaller sample and n 2 be the sample size of the larger sample Procedure for assigned rank to data values: First combine both the samples. Arrange the data values in ascending order. Rank each of the data value in sequential order. The rank for each of tied data is computed as, First assign the sequential position ranks for all the values that are same. Take the mean of all the position ranks that are assigned for same data values. Assign the mean rank as the rank position for all the tied data. The assigned mean rank is used in calculating the test statistic. The ranks are, Meters Rank Stock 1.58 1 B 1.94 2 A 1.96 3 B 2.1 4 A 2.13 5 B 2.26 6 A 2.37 7 A 2.44 8 B 2.52 9 B 2.58 10 A 2.71 11 B 2.74 12 A 2.77 13 B 2.78 14 B 2.81 15 A 2.86 16 B 2.88 17 A 2.91 18 B 2.94 19 A 3.02 20 B 3.11 21 A 3.41 22 A The smaller sample is 11 which corresponds the both ‘ A ’, and ‘ B ’. That is, n 1 = 11 , n 2 = 11 . The value of R is, R = 2 + 4 + 6 + 7 + 10 + 12 + 15 + 17 + 19 + 21 + 221 = 135 The value of R is 135

Understandable Statistics: Concepts and Methods

12th Edition

ISBN: 9781337119917

Author: Charles Henry Brase, Corrinne Pellillo Brase

Publisher: Cengage Learning

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Identify whether the distributions of growths are different for root stocks A and B.

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Understandable Statistics: Concepts and Methods

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Identify whether the distributions of growths are different for root stocks A and B . Interpret the results.

Solution Summary: The author concludes that there is no evidence that the distributions of growths are different for root stocks A and B

Videos

Identify whether the distributions of growths are different for root stocks A and B.

Interpret the results.

Chapter 11 Solutions

Identify whether the distributions of growths are different for root stocks A and B . Interpret the results.

Solution Summary: The author concludes that there is no evidence that the distributions of growths are different for root stocks A and B

Videos

Identify whether the distributions of growths are different for root stocks A and B. Interpret the results.

Chapter 11 Solutions

Identify whether the distributions of growths are different for root stocks A and B.

Interpret the results.