Construct the Indicated Confidence Interval for the Difference Between the Two

question 93

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 paint manufacturer wished to compare the
Drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9
Cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The
Summary statistics are as follows. $$\begin{array} { | c | c | } \hline \text { Type A } & \text { Type B } \\\hline \bar { x } _ { 1 } = 75.7 \mathrm { hrs } & \bar { x } _ { 2 } = 64.3 \mathrm { hrs } \\\hline s _ { 1 } = 4.5 \mathrm { hrs } & s _ { 2 } = 5.1 \mathrm { hrs } \\\hline n _ { 1 } = 11 & n _ { 2 } = 9 \\\hline\end{array}$$ Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint type A ar the mean drying time for paint type $B$ .

• A) \(5.78\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < 17.02\) hrs
• B) \(6.08\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < 16.72\) hrs
• C) \(5.92\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < 16.88\) hrs
• D) \(5.85 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.95 \mathrm { hrs }\)

---

Definitions:

Higher Resources

Refers to the availability of increased or superior assets, whether financial, material, or human, for the purpose of achieving greater objectives or improving operations.

Social Conduct

Refers to behaviors and actions that are considered acceptable and appropriate according to societal norms and values.

Behaviors

Actions or reactions of an individual or group in response to external or internal stimuli, often studied in psychology and sociology to understand and predict patterns.

Environment

The surroundings or conditions in which a person, animal, or plant lives or operates, including natural, social, and cultural factors.