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Which of the following z statistics has the smallest p value? O - 2.01 1.78 0.50 - 0.23

Which of the following z statistics has the smallest p value? O - 2.01 1.78 0.50 - 0.23

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...
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### Question Which of the following z statistics has the smallest *p* value? ### Options - ○ - 2.01 - ○ 1.78 - ○ 0.50 - ○ - 0.23 ### Explanation This question is designed to test the understanding of z statistics and *p* values. In statistical hypothesis testing, the *p* value is the probability of obtaining test results at least as extreme as the observed data, assuming that the null hypothesis is true. A smaller *p* value indicates stronger evidence against the null hypothesis. To find the smallest *p* value, one needs to consider the absolute value of the z statistic because the *p* value is associated with the extremeness of the z score. The larger the absolute value of the z statistic (whether positive or negative), the smaller the *p* value. In this question, the absolute values of the z statistics are as follows: - |-2.01| = 2.01 - |1.78| = 1.78 - |0.50| = 0.50 - |-0.23| = 0.23 Therefore, the z statistic with the smallest *p* value is - 2.01, as 2.01 is the largest absolute value among the given options.
Transcribed Image Text:### Question Which of the following z statistics has the smallest *p* value? ### Options - ○ - 2.01 - ○ 1.78 - ○ 0.50 - ○ - 0.23 ### Explanation This question is designed to test the understanding of z statistics and *p* values. In statistical hypothesis testing, the *p* value is the probability of obtaining test results at least as extreme as the observed data, assuming that the null hypothesis is true. A smaller *p* value indicates stronger evidence against the null hypothesis. To find the smallest *p* value, one needs to consider the absolute value of the z statistic because the *p* value is associated with the extremeness of the z score. The larger the absolute value of the z statistic (whether positive or negative), the smaller the *p* value. In this question, the absolute values of the z statistics are as follows: - |-2.01| = 2.01 - |1.78| = 1.78 - |0.50| = 0.50 - |-0.23| = 0.23 Therefore, the z statistic with the smallest *p* value is - 2.01, as 2.01 is the largest absolute value among the given options.
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