Preliminary Data Analyses Indicate That You Can Reasonably Use Nonpooled

question 51

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 wishes to compare the drying times of two different types of paint. Independent 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 minutes)were recorded. The summary statistics are as follows. $\begin{array} { r | r } \text { Type A } & \text { Type B } \\ \hline \bar { x } _ { 1 } = 75.4 & \bar { x } _ { 2 } = 64.7 \\ \mathrm {~s} _ { 1 } = 4.5 & \mathrm {~s} _ { 2 } = 5.1 \\ \mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 9 \end{array}$
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? Perform a t-test at the 1% significance level. Use the P-value approach.

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Definitions:

Cognitive Development

The process by which a person perceives, thinks, and gains understanding of their world through the interaction and influence of genetic and learned factors.

Piaget's Theory

A comprehensive theory developed by Jean Piaget that explains the stages of cognitive development in children, focusing on how they acquire, construct, and use knowledge.

Resistant Attachment

A type of attachment pattern observed in children, characterized by reluctance to explore and distress upon separation from the caregiver, often mixed with resistance upon reunion.

Ainsworth's Strange Situation

An experimental procedure created to assess attachment styles in children by observing their behavior when separated and reunited with their caregivers.