Determine Whether the Samples Are Independent or Dependent Construct a 95% Confidence Interval For

question 73

Multiple Choice

Determine whether the samples are independent or dependent.
-A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. $$\begin{array} { | c | c c | } \hline \text { College A } & { \text { College B } } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 & \\3.4 & & \\\hline\end{array}$$ Construct a 95% confidence interval for $$\mu _ { 1 } - \mu _ { 2 }$$ , the difference between the mean GPA of college A students
And the mean GPA of college B students. (Note: $\bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , \mathrm {~s} _ { 1 } = 0.4357$ , $\mathrm { s } _ { 2 } = 0.5485$ .)

• A) \(- 0.75 < \mu _ { 1 } - \mu _ { 2 } < 0.10\)
• B) \(- 0.78 < \mu _ { 1 } - \mu _ { 2 } < 0.13\)
• C) \(- 0.81 < \mu _ { 1 } - \mu _ { 2 } < 0.15\)
• D) \(- 0.70 < \mu _ { 1 } - \mu _ { 2 } < 0.05\)

---

Definitions:

Cognitive Therapy

A form of psychotherapy that aims to change patterns of thinking or behavior that are problematic, thus altering emotional states and dealing with disorders.

Bipolar Disorder

A mental health condition marked by extreme mood swings that include emotional highs (mania or hypomania) and lows (depression).

Dodo Bird Verdict

A metaphor stemming from Alice in Wonderland and used in psychology to suggest that different forms of therapy are equally effective.

Psychotherapy

A treatment method for mental health conditions involving talking with a mental health professional to explore thoughts, feelings, and behaviors to achieve desired change.