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"Cramming" Is a Technique Often Used by Students to Prepare

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"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1) is shown below for the five students.  Cramming  is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1) is shown below for the five students.   What is the mean of the Wilcoxon signed rank test statistic,W<sup>+</sup>,under the null hypothesis that there is no difference? A) 3 B) 12 C) 15 D) None of the above What is the mean of the Wilcoxon signed rank test statistic,W+,under the null hypothesis that there is no difference?


Definitions:

Payroll Tax

Levies placed on both employers and employees, computed based on a fraction of the wages that employers distribute to their workforce.

Income Levels

The categories of earnings that individuals or households fall into, typically used to analyze economic and demographic data.

Tax Incidence

The study of who ultimately pays the tax or bears the burden of tax, which can differ from the entity that initially pays the tax.

Total Burden

The complete impact, often in terms of costs or taxes, borne by society or specific groups within it.

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