Two Independent Samples of Sizes 35 and 40 Are Randomly $\mu _ { 1 } - \mu _ { 2 }$

question 4

Short Answer

Two independent samples of sizes 35 and 40 are randomly selected from two normally distributed populations. Assume that the population variances are unknown but equal. In order to test the difference between the population means, $\mu _ { 1 } - \mu _ { 2 }$ , the sampling distribution of the sample mean difference, $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ , is: $\begin{array}{|l|l|}\hline A&\text {normally distributed. }\\\hline B&\text {\( t \)-distributed with 75 degrees of freedom. }\\\hline C&\text {\( t \)-distributed with 73 degrees of freedom. }\\\hline D&\text {\( F \)-distributed with 34 and 39 degrees of freedom. }\\\hline\end{array}$

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Definitions:

Long-Term U.S. Treasury Bonds

Bonds issued by the U.S. government with a maturity of typically 20 or 30 years, considered to be one of the safest long-term investments.

EAR

stands for Effective Annual Rate, a calculation that reflects the annual interest on an investment or loan, taking into account the effect of compounding interest.

APR

Annual Percentage Rate, which represents the annualized cost of credit including interest and other charges, helping consumers compare the cost of loans.

Continuous Compounding

Continuous compounding refers to the process of calculating interest on an investment, where the interest amount is reinvested and earns additional interest continuously, leading to exponential growth.