Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

question 48

Multiple Choice

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-When performing a hypothesis test for the ratio of two population variances, the upper critical F value is denoted $\mathrm { F } _ { \mathrm { R } }$ . The lower critical $\mathrm { F }$ value, $\mathrm { F } _ { \mathrm { L } }$ , can be found as follows: interchange the degrees of freedom, and then take the reciprocal of the resulting $F$ value found in table $\mathrm { A } - 5$ . $\mathrm { F } _ { \mathrm { R } }$ can be denoted $\mathrm { F } _ { \alpha / 2 }$ and $\mathrm { F } _ { \mathrm { L } }$ can be denoted $\mathrm { F } _ { 1 - \alpha / 2 }$ .
Find the critical values $\mathrm { F } _ { \mathrm { L } }$ and $\mathrm { F } _ { \mathrm { R } }$ for a two-tailed hypothesis test based on the following values: $\mathrm { n } _ { 1 } = 4 , \mathrm { n } _ { 2 } = 8 , \alpha = 0.05$

• A) \(0.1112,5.0453\)
• B) \(0.1703,5.8898\)
• C) \(0.0684,5.8898\)
• D) \(0.1211,4.3541\)

---

Definitions:

Human Factors Psychologist

A specialist in psychology focused on improving and understanding how people interact with products, systems, and environments to enhance performance and safety.

Performance Psychologist

A professional who applies psychological principles to enhance the performance, motivation, and mental well-being of athletes.

Performance Appraisal

The process of evaluating an employee's job performance and productivity to provide feedback and guide future development.

Directive Style

A leadership or management approach where decisions and tasks are explicitly dictated and controlled.