Write Hypotheses for the Two-Sample T-Test $\mathrm { H } _ { 0 : } \mu _ { 1 } - \mu _ { 2 } = 0$

question 18

Short Answer

Write hypotheses for the two-sample t-test.
-Data were collected on annual personal time (in hours) taken by a random sample of 16
Women (group1) and 7 men (group 2) employed by a medium sized company. The women
Took an average of 24.75 hours of personal time per year with a standard deviation of 2.84
Hours. The men took an average of 21.89 hours of personal time per year with a standard
Deviation of 3.29 hours. The Human Resources Department believes that women tend to
Take more personal time than men because they tend to be the primary child care givers in
The family. The correct null and alternative hypotheses to test this belief are A. $\mathrm { H } _ { 0 : } \mu _ { 1 } - \mu _ { 2 } = 0$ and $\mathrm { H } _ { \mathrm { A } : } \mu _ { 1 } - \mu _ { 2 } < 0$ .
B. $H _ { 0 : } \mu _ { 1 } - \mu _ { 2 } = 0$ and $H _ { \mathrm { A } : } \mu _ { 1 } - \mu _ { 2 } \neq 0$ .
C. $\mathrm { H } _ { 0 : } \mu _ { 1 } - \mu _ { 2 } = 0$ and $\mathrm { H } _ { \mathrm { A } : } \mu _ { 1 } - \mu _ { 2 } > 0$ .
D. $\mathrm { H } _ { 0 } : \mu _ { 1 } - \mu _ { 2 } > 0$ and $\mathrm { H } _ { \mathrm { A } } : \mu _ { 1 } - \mu _ { 2 } < 0$ .
E. None of the above.

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Definitions:

Shareholders

Individuals or entities that own one or more shares of stock in a corporation, making them the owners of the corporation to the extent of the shares they hold.

Sole Proprietorship

A business in which one person (sole proprietor) is in control of the management and profits.

Management

The process of planning, organizing, leading, and controlling resources to achieve organizational goals.

Profits

The financial gain realized when the revenue generated from business activities exceeds the expenses, taxes, and costs involved in maintaining the operation.