State What the Given Confidence Interval Suggests About the Two

question 192

Multiple Choice

State what the given confidence interval suggests about the two population means.
-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 the difference between the mean GPA of college A students and the
Mean GPA of college B students. (Note: $\bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , s _ { 1 } = 0.4357 , \mathrm {~s} _ { 2 } = 0.5485$ .)

• A) \(- 0.91 < \mu _ { 1 } - \mu _ { 2 } < 0.25\)
• B) \(- 0.65 < \mu _ { 1 } - \mu _ { 2 } < - 0.01\)
• C) \(- 0.81 < \mu _ { 1 } - \mu _ { 2 } < 0.15\)
• D) \(- 0.72 < \mu _ { 1 } - \mu _ { 2 } < 0.07\)

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Definitions:

Cash Payback Period

The duration it takes for an investment to generate an amount of cash equal to the initial investment cost.

Salvage Value

The estimated residual value of an asset at the end of its useful life, representing what it could be sold for or its scrap value.

Straight-Line

A depreciation method that equally spreads the cost of an asset over its useful life.

Annual Rate of Return

The yearly profit from an investment, expressed as a percentage of the original investment.