Determine Whether the Samples Are Independent or Dependent Use a 005 Significance Level to Test the Claim That the Mean

question 57

Essay

Determine whether the samples are independent or dependent.
-A researcher was interested in comparing the amount of time (in hours) spent watching television by women
and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was
asked how many hours he or she had watched television during the previous week. The summary statistics are
as follows. $$\begin{array} { | l | l | } \hline \text { Women } & \text { Men } \\\overline { \mathrm { x } } _ { 1 } = 12.5 \mathrm { hr } & \overline { \mathrm { x } } _ { 2 } = 13.8 \mathrm { hr } \\\mathrm { s } _ { 1 } = 3.9 \mathrm { hr } & \mathrm { s } _ { 2 } = 5.2 \mathrm { hr } \\\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 17 \\\hline\end{array}$$ Use a 0.05 significance level to test the claim that the mean amount of time spent watching television by women
is smaller than the mean amount of time spent watching television by men. Use the traditional method of
hypothesis testing.

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Definitions:

Variable Costs

Charges that fluctuate in accordance with the scale of production or total volume produced.

Special Equipment

Tools, machinery, or devices designed for specific tasks or operations, often requiring specialized knowledge or skills to use effectively.

Contribution Margin

The surplus of sales revenue over variable costs, showing the extent to which revenue aids in covering fixed costs and generating profit.

Financial Advantage

The benefit gained in a financial context, such as lower costs, higher revenues, or competitive superiority.