Construct the Indicated Confidence Interval for the Difference Between the Two

question 14

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.
$\begin{array}{|l|l|}\hline {\text { Type A }} & {\text { Type B }} \\\hline \bar{x}_{1}=75.7 \mathrm{hrs} & \bar{x}_{2}=64.3 \mathrm{hrs} \\\hline s_{1}=4.5 \mathrm{hrs} & s_{2}=5.1 \mathrm{hrs} \\\hline n_{1}=11 & n_{2}=9 \\\hline\end{array}$

Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint type A and the mean drying time for paint type B.

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

---

Definitions:

Bed-Bound Patient

An individual who is unable to leave their bed due to medical conditions or frailty.

Dry Skin

A common condition where skin lacks moisture or natural oils, often leading to itching and flakiness.

Moisturizers

Products designed to hydrate the skin, reducing dryness and creating a protective layer to retain moisture.

Ultraviolet Light

A type of electromagnetic radiation with a wavelength shorter than that of visible light but longer than X-rays, often used for sterilization.