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Procedures for Handling Ties In the sign test procedure

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola ISBN: 9780321836960 18

Solution for problem 21BB Chapter 13.2

Elementary Statistics | 12th Edition

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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Elementary Statistics | 12th Edition

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Problem 21BB

Procedures for Handling Ties In the sign test procedure described in this section, we exclude ties (represented by 0 instead of a sign of + or ?). A second approach is to treat half of the 0s as positive signs and half as negative signs. (If the number of 0s is odd, exclude one so that they can be divided equally.) With a third approach, in two-tailed tests make half of the 0s positive and half negative; in one-tailed tests make all 0s either positive or negative, whichever supports the null hypothesis. Repeat Example 4 using the second and third approaches to handling ties. Do the different approaches lead to very different results?

Step-by-Step Solution:

Solution 21BB Step 1 In the second approach, to treat half of the zero’s as positive signs and the other half as negative signs. With a third approach in two tailed tests. Let us denote negative sign (-) for temperature below 98.6 F and positive sign (+) for temperature above 98.6 F, we have 15 zero’s we are excluding one zero in order to make it even, now we get 7 zero’s as positive and 7 zero’s as negative. Now, Positive signs = 30 Negative signs = 75 Now, the Test Statistic is the less frequent sign i.e., positive sign = 30 Therefore, x = 30 is the required value of test statistic. Hence for sign test the required sample size used is 105 i.e., n = 30 + 75 = 105 which is greater than 25 (n 25). Step 3 Hence the Test Statistic x = 20 can be converted to the Test Statistic as shown below (x + 0.5) ( ) z = n 2 2 (30 + 0.5) 2() z = 105 2 z = (30.5) (52.5) 5.12 On substitution we get, z = -1.645 is the required test statistic. From A-2 table, the critical values are z = -1.645 and z -1.645 for one tailed test(left tailed test) at 5% level of significance. From the above figure, we see that z = -4.29 does not fall within the critical region. Hence we reject the Null hypothesis and conclude that there is sufficient evidence to 0 0 claim that the the median body temperature is less than 98.6 F and it is not equal to 98.6 F.

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Chapter 13.2, Problem 21BB is Solved
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Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

The answer to “Procedures for Handling Ties In the sign test procedure described in this section, we exclude ties (represented by 0 instead of a sign of + or ?). A second approach is to treat half of the 0s as positive signs and half as negative signs. (If the number of 0s is odd, exclude one so that they can be divided equally.) With a third approach, in two-tailed tests make half of the 0s positive and half negative; in one-tailed tests make all 0s either positive or negative, whichever supports the null hypothesis. Repeat Example 4 using the second and third approaches to handling ties. Do the different approaches lead to very different results?” is broken down into a number of easy to follow steps, and 113 words. This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12. Since the solution to 21BB from 13.2 chapter was answered, more than 285 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 21BB from chapter: 13.2 was answered by , our top Statistics solution expert on 03/15/17, 10:30PM. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. This full solution covers the following key subjects: half, Negative, ties, Positive, approach. This expansive textbook survival guide covers 121 chapters, and 3629 solutions.

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