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:

Weaknesses

Areas of lesser ability or strength in an individual, organization, or system that may hinder performance or achievement.

Reciprocal Determinism

A concept in psychology that suggests individual behavior, environment, and cognition are interlinked and influence each other.

B.F. Skinner

An American psychologist known for his work in behaviorism, emphasizing the role of reinforcement and punishment in shaping behavior.

Bandura

Albert Bandura was a psychologist best known for his work on social learning theory and for emphasizing the role of observational learning, self-efficacy, and reciprocal determinism in psychology.