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\section*{Homework 7 - Aidan Sharpe}

\subsection*{Problem 1}
A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to decrease the energy absorption of the film, and he believes this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film absorption (in microjules per square inch) is measured. For the 25-mil film the sample data result is $\bar{x}_1 = 1.17$ and $s_1 = 0.10$. While for the 20-mil film, the data yield $\bar{x}_2 = 1.07$ and $s_2 = 0.09$. Note that an increase in film speed would lower the value of the observation in microjules per square inch. Do the data support the claim that reducing the film thickness increases the mean speed of the film? Use $\alpha = 0.10$ and assume the two population variances are equal and the underlying population of film speed is normally distributed.

\begin{itemize}
    \item[$H_0$:] $\mu = \mu_0$
    \item[$H_a$:] $\mu < \mu_0$
\end{itemize}


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