Construct the Indicated Confidence Interval for the Difference Between the Two

question 21

Multiple Choice

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.
-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.

$\begin{array}{c|cc}\text { College A } & \text { College B } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 & \\3.4 & &\end{array}$
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) \(- 0.70 < \mu _ { 1 } - \mu _ { 2 } < 0.05\)
• B) \(- 0.75 < \mu _ { 1 } - \mu _ { 2 } < 0.10\)
• C) \(- 0.81 < \mu _ { 1 } - \mu _ { 2 } < 0.15\)
• D) \(- 0.78 < \mu _ { 1 } - \mu _ { 2 } < 0.13\)

Comprehend the growth and challenges of part-time employment in Canada.

Grasp the concept of deskilling in the workplace and its implications for profit and productivity.

Understand the role and impact of licensing practices and occupational associations.

Analyze the dynamics of the labour market in Canada, including shifts in part-time work rates and emerging growth sectors.

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Definitions:

Marginal Value

Marginal value is the additional satisfaction or utility gained from consuming one more unit of a good or service.

Price Discriminate

The practice of selling the same product to different buyers at different prices based on their willingness or ability to pay.

Demand Curves

A graphical representation showing the relationship between the price of a good and the quantity of that good consumers are willing and able to purchase, typically downward sloping.

Marginal Value

The extra benefit or pleasure derived from using or making an additional unit of a product or service.