Preliminary Data Analyses Indicate That You Can Reasonably Use Nonpooled

question 3

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 researcher was interested in comparing the amount of time spent watching television by women and by men. Independent random samples of 14 women and 17 men were selected and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows: $$\begin{array} { r | r } \text { Sample } 1 \text { (women) } & \text { Sample } 2 \text { (men) } \\ \hline \overline { \mathrm { x } } _ { 1 } = 12.3 & \overline { \mathrm { x } } _ { 2 } = 14.1 \\ \mathrm {~s} _ { 1 } = 3.9 & \mathrm {~s} _ { 2 } = 5.2 \\ \mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 17 \end{array}$$ At the 5% significance level, do the data provide sufficient evidence to conclude that the mean amount of time spent watching television by women is less than the mean amount of time spent watching television by men? Use the P-value approach.

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Definitions:

Standard Deviation

The statistical measure that quantifies the dispersion or variability within a data set.

Mean

The arithmetic average of a set of numbers, calculated by adding them together and dividing by the count of the numbers.

Z-score

A numerical metric indicating how a specific value compares to the average of a dataset, expressed by the number of standard deviations away from that average.

Standard Deviation

An indicator of the spread or variability within a data set; where a small standard deviation indicates values closely clustered around the average, and a large standard deviation suggests they are widely scattered.