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

question 17

Essay

Preliminary data analyses indicates that use of a paired t-test is reasonable. Perform the hypothesis test by using eitherthe critical-value approach or the P-value approach as indicated. Assume that the null hypothesis is $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-Five students took a math test before and after tutoring. Their scores were as follows. $$\begin{array} { c | r r r r r } \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\ \hline \text { Before } & 71 & 78 & 73 & 72 & 75 \\ \hline \text { After } & 75 & 87 & 71 & 75 & 87 \end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the mean score before tutoring differs from the mean score after tutoring? Use the P-value approach.

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Definitions:

Factory Overhead

Costs associated with operating a factory that are not directly tied to a specific product or activity, such as maintenance, utilities, and salaries for management.

Work in Process

Work in Process (WIP) inventory includes partially finished goods that are still undergoing the manufacturing process and are not yet ready for sale to customers.

Cost of Goods Sold

The direct costs attributable to the production of the goods sold by a company, including the cost of the materials and labor directly used to create the product.

Time Ticket

A time ticket is a document or record used to track the amount of time an employee spends on various tasks or projects, typically for billing or payroll purposes.