The Table Shows the Number of Pitchers with E $3.5$ In a Random Sample of Sixty Pitchers from the National

Multiple Choice

The table shows the number of pitchers with E.R.A's below $3.5$ in a random sample of sixty pitchers from the National League and in a random sample of fifty-two pitchers from the American League. Assume that you plan to use a significance level of $\alpha = 0.05$ to test the claim that $\mathrm { p } _ { 1 } \neq \mathrm { p } _ { 2 }$ . Find the critical value(s) for this hypothesis test. Do the data support the claim that the proportion of National League pitchers with an E.R.A. below $3.5$ differs from the proportion of American League pitchers with an E.R.A. below 3.5?
$\begin{array}{lcc}\hline & \text { National League } & \text { American League } \\\hline \text { Number of pitchers in sample } & 60 & 52 \\\text { Number of pitchers with E.R.A. below 3.5 } & 16 & 10 \\\hline\end{array}$

A) $\mathrm { z } = \pm 1.96$ ; no
B) $z = \pm 1.645$ ; yes
C) $\mathrm { z } = \pm 2.575$ ; no
D) $z = 1.645$ ; yes