Determine Whether the Samples Are Independent or Dependent Construct a 90% Confidence Interval For

question 52

Multiple Choice

Determine whether the samples are independent or dependent.
-A researcher was interested in comparing the heights of women in two different countries. Independent simple random samples of 9 women from country A and 9 women from country B yielded the following heights (in
Inches) . $$\begin{array} { | c | c | } \hline \text { Country A } & \text { Country B } \\\hline 64.1 & 65.3 \\66.4 & 60.2 \\61.7 & 61.7 \\62.0 & 65.8 \\67.3 & 61.0 \\64.9 & 64.6 \\64.7 & 60.0 \\68.0 & 65.4 \\63.6 & 59.0 \\\hline\end{array}$$ Construct a 90% confidence interval for $$\mu _ { 1 } - \mu _ { 2 }$$ , the difference between the mean height of women in country A
And the mean height of women in country B. (Note: $\bar { x } _ { 1 } = 64.744$ in., $\bar { x } _ { 2 } = 62.556$ in., $s _ { 1 } = 2.192$ in., $s _ { 2 } = 2.697$ in.)

• A) \(0.16 \mathrm { in } . < \mu _ { 1 } - \mu _ { 2 } < 4.22 \mathrm { in }\).
• B) \(0.14\) in. \(< \mu _ { 1 } - \mu _ { 2 } < 4.24\) in.
• C) \(0.17\) in. \(< \mu _ { 1 } - \mu _ { 2 } < 4.21\) in.
• D) \(0.15\) in. \(< \mu _ { 1 } - \mu _ { 2 } < 4.23\) in.

---

Definitions:

Stockholders' Equity

The residual interest in the assets of a corporation that remains after deducting its liabilities, often referred to as shareholders' equity.

Stock Dividend

A dividend payment to shareholders in the form of additional shares rather than cash.

Additional Paid-in Capital

The amount of capital paid by investors above the par value of the stock during equity issuance.

Retained Earnings

The portion of net earnings not paid out as dividends but retained by the company to reinvest in its core business or to pay debt.