Determine Whether the Samples Are Independent or Dependent Construct a 98% Confidence Interval For

question 9

Multiple Choice

Determine whether the samples are independent or dependent.
-A researcher was interested in comparing the salaries of female and male employees at a particular company. Independent simple random samples of 8 female employees and 15 male employees yielded the following
Weekly salaries (in dollars) . $$\begin{array} { r | r r } \text { Female } & \text { Male } & \\\hline 495 & 722 & 518 \\760 & 562 & 904 \\556 & 880 & 1150 \\904 & 520 & 805 \\520 & 500 & 480 \\1005 & 1250 & 970 \\743 & 750 & 605 \\660 & 1640 &\end{array}$$
Construct a 98% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ the difference between the mean weekly salary of female Employees and the mean weekly salary of male employees at the company. $\left( \text { Note: } \bar { x } _ { 1 } = \$ 705.38 , \bar { x } _ { 2 } = \$ 817.07 , \mathrm {~s} _ { 1 } = \$ 183.86 , \mathrm {~s} 2 = \$ 330.15 . \right)$

• A) \(- \$ 385 < \mu _ { 1 } - \mu _ { 2 } < \$ 164\)
• B) \(- \$ 431 < \mu _ { 1 } - \mu _ { 2 } < \$ 208\)
• C) \(- \$ 383 < \mu _ { 1 } - \mu _ { 2 } < \$ 159\)
• D) \(- \$ 382 < \mu _ { 1 } - \mu _ { 2 } < \$ 158\)

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Definitions:

Hyperbolic Discounting

A behavioral economics theory suggesting that people are more likely to choose smaller, immediate rewards over larger, later rewards, displaying a decreasing rate of time preference.

Hyperbolic Discounting

A behavioral economics theory, describing how people tend to choose smaller, immediate rewards over larger, delayed ones.

Next Year's Salary

The amount of money or compensation that an individual is projected to earn in the coming year.

Current Salary

The present rate of compensation for employment before any deductions like taxes or retirement contributions.