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:

Median

The middle value in a list of numbers sorted in ascending or descending order, or the average of the two middle numbers when the list has an even number of values.

Mathematical Average

The sum of a list of numbers divided by the count of numbers in the list, commonly referred to as the mean.

Median

The middle value in a data set when it is arranged in ascending or descending order, effectively dividing the data set in half.

Set Of Data

A collection of values or observations, that can be analyzed to find patterns and draw conclusions.