ENOCH CUL
Lreakal
A purchasing manaper for a large unlversity is investicating which brand of LCD profecter to purchase to eculo thelr dassrocms. Of malor concem is the Iongevity of the light bulbs used in the projectors. The purchasing marager has narrowed down the cholce of prejectsr to two brands, Infocus and Prosima, and wishes to determise if there is any difference between the two brands in the mean Ketime of the bellot ased.
The purchasling manager obtalied nine prolectors of each brand for testing over the last several academic terms. The sumber of hours the bulbs lasted on tach of the nine projectors is given in the table.
\begin{tabular}{|c|c|}
\hline & \\
\hline tulerat & \( 985,535,560,785,586,722,995,1136,776 \) \\
\hline Howing & \( 710,551,993,1069,919,775, \$ 34,366,930 \) \\
\hline
\end{tabular}
Send daks to calculatsr
Sered dide to Eaced
Assume that the two populations of lifedmes are normalleditribsted and that the pooulation varlances are equal.
Can we cendude, at the 0.10 ifst of slanificance, that \( \mu_{1} \), the mean lifetime of light belbs in trifocus prolectors, difers from \( \mu_{2} \), the mean lifedime of light bulbs In Froxima prodectors?
Aerform a two-taled test. Then cemplete the parts below.
Camry your intermediate computations to three or more decimal places and round vour answers as specified in the table. (if necessary, consult a liat of formias.)
(a) State the nullysokhesls \( H_{0} \) and the altemathre hockthesls \( H_{1} \).
\[
\begin{array}{l}
\boldsymbol{H}_{0}: \square \\
H_{1}=\square
\end{array}
\]
(b) Determine the trpe of testatarlatic to use.
(Choose ene)
(c) Find the value of the test stathstic. (Round to three or more decimal places.)
\( \square \)
(d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.)
\( \square \) and \( \square \)
(4) Can we conclude that \( \mu_{1} \), the mean IIfetime of light bults in Intocws prolectors, differs from \( \mu_{2} \), the mean lifetime of light balbs in Frovima projecters?
Yes Ns
