Preliminary Data Analyses Indicate That You Can Reasonably Use Nonpooled

question 36

Essay

Preliminary data analyses indicate that you can reasonably use nonpooled t-procedures on the given data. Apply anonpooled t-test to perform the required hypothesis test, using either the critical-value approach or the P-value approachas indicated.
-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. $$\begin{array} { r | r } \ { \text { Type A } } & \text { Type B } \\\hline\bar{{ x} _ { 1 }} = 74.7 & \bar{ { x } _ { 2 } }= 64.4 \\\mathrm {~s} _ { 1 } = 4.5 & \mathrm {~s} _ { 2 } = 5.1 \\\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 9\end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the mean drying time for type A differs from the mean drying time for type B? Use the critical-value approach.

---

Definitions:

Cephalocaudal

A principle of physical growth that describes how growth starts at the head and upper body parts and then proceeds to the rest of the body.

Development

The process of change and growth in physical, cognitive, and social aspects over the lifespan.

Head

The upper part of the human body, containing the brain, eyes, ears, nose, and mouth.