Solve the Problem $\alpha = 0.05$ 05 to Test the Claim That

Multiple Choice

Solve the problem.
-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 $\alpha = 0.05$ 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? $\begin{array}{lcc}\hline & \text { National League } & \text { American League } \\\hline \text { Number of pitchers in sample } & 60 & 52 \\\text { Number of pitchers with E.R.A. below 3.5 } & 10 & 8 \\\hline\end{array}$

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