Preliminary Data Analyses Indicates That Use of a Paired Wilcoxon $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$

question 64

Essay

Preliminary data analyses indicates that use of a paired Wilcoxon signed-rank test is reasonable. Perform the hypothesistest by using a paired Wilcoxon signed-rank test. Assume that the null hypothesis is $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-Students take a math test before and after tutoring. The data for a random sample of students is given below. $$\begin{array} { c | l l l l l l l l l } \text { Before } & 54 & 72 & 59 & 82 & 46 & 80 & 63 & 36 & 44 \\ \hline \text { After } & 68 & 70 & 67 & 78 & 55 & 90 & 63 & 52 & 40 \end{array}$$ At the 2.5% level of significance, do the data provide sufficient evidence to conclude that the mean score before the tutoring is lower than the mean score after the tutoring?

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Definitions:

Number Of Symptoms

Refers to the quantitative count of signs or symptoms displayed by an individual which are indicative of a particular condition or disorder.

Type I Schizophrenia

A subtype of schizophrenia characterized by the prominence of positive symptoms such as delusions and hallucinations.

Type II Schizophrenia

A subtype of schizophrenia characterized by a predominance of negative symptoms such as emotional flatness and lack of motivation.

Positive Symptoms

Refers to an excess or distortion of normal functions, often observed in disorders such as schizophrenia, including hallucinations or delusions.