Preliminary Data Analyses Indicate That You Can Reasonably Consider the Assumptions

question 1

Essay

Preliminary data analyses indicate that you can reasonably consider the assumptions for using the Mann-Whitney testsatisfied. Assume that the null hypothesis is $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$ . Use the Mann-Whitney test to carry out the requiredhypothesis test.
-A researcher was interested in investigating how much people read in their spare time and, in particular, whether people who own a personal computer read less in their spare time than those who do not own a computer. She selected independent simple random samples of 7 computer owners and 9 noncomputer owners, and she asked each person how many hours he or she had spent reading non-work-related books during the previous week. The results are as follows. $$\begin{array} { r | r } \text { Computer Owners } & \text { Noncomputer Owners } \\ \hline 1.7 & 1.8 \\ 0 & 6.6 \\ 2.6 & 0.3 \\ 0.9 & 0 \\ 6.2 & 0.2 \\ 0 & 2.3 \\ 0.5 & 8.8 \\ & 2.2 \\ & 1.4 \end{array}$$ At the 2.5% significance level, do the data provide sufficient evidence to conclude that the mean weekly reading time for computer owners is lower than the mean weekly reading time for noncomputer owners?

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Definitions:

Relative Frequency Histograms

Graphs that display the proportion or percentage of observations within each category/bin of the data.

Probability Histogram

A graphical representation that displays the probability distribution of a discrete variable.

Simple Events

Events in probability that consist of a single outcome and cannot be broken down further.

Mutually Exclusive

Refers to events that cannot happen at the same time, meaning the occurrence of one event excludes the possibility of the other.