Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

question 59

Essay

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-A test of abstract reasoning is given to a random sample of students before and after they completed a formal
logic course. The results are given below. At the 0.05 significance level, test the claim that the mean score is not
affected by the course. $$\begin{array} { l l l l l l l l l l l } \text { Before } & 74 & 83 & 75 & 88 & 84 & 63 & 93 & 84 & 91 & 77 \\\hline \text { After } & 73 & 77 & 70 & 77 & 74 & 67 & 95 & 83 & 84 & 75\end{array}$$

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Definitions:

Merchandise Purchases

Transactions involved in buying goods for resale in the normal course of business, typically constituting a significant expense for retail companies.

Physical Inventory

Physical Inventory involves a manual count of all physical goods a company has in stock at a specific point in time to ensure accuracy of inventory records.

Income Statement

A financial statement that shows a company's revenues and expenses over a specific period of time, resulting in a net profit or loss.

Ending Inventory

The value of goods that a company has in stock at the end of its fiscal year, calculated as the beginning inventory plus purchases minus the cost of goods sold.