A Supermarket Sells Rotisserie Chicken at a Fixed Price Per $\begin{array} { l l l l l l l l l l } 4.4 & 4.7 & 4.6 & 4.4 & 4.5 & 4.3 & 4.6 & 4.5 & 4.6 & 4.9 \end{array}$

A supermarket sells rotisserie chicken at a fixed price per chicken rather than by the
weight of the chicken. The store advertises that the average weight of their chickens is 4.6
pounds. A random sample of 30 of the storeʹs chickens yielded the weights (in pounds)
shown below. $\begin{array} { l l l l l l l l l l } 4.4 & 4.7 & 4.6 & 4.4 & 4.5 & 4.3 & 4.6 & 4.5 & 4.6 & 4.9 \end{array}$
$\begin{array} { l l l l l l l l l l } 4.6 & 4.8 & 4.3 & 4.4 & 4.7 & 4.5 & 4.2 & 4.3 & 4.1 & 4.0 \end{array}$
$\begin{array} { l l l l l l l l l l l } 4.5 & 4.6 & 4.2 & 4.4 & 4.7 & 4.8 & 5.0 & 4.2 & 4.1 & 4.5 \end{array}$
Find and interpret the $p$ -value in a test of $H _ { 0 } : \mu = 4.6$ against $H _ { \mathrm { a } } : \mu < 4.6$ .