Question

(20 points) A random sample of =1200 n = 1200 registered voters and found that 620 would vote for the Republican candidate in a state senate race. Let p represent the proportion of registered voters who would vote for the Republican candidate. Consider testing 0:=.50 H 0 : p = .50 :>.50 H a : p > .50 (a) The test statistic is z =

Answer 1

Answer:

The test statistic is Z = 1.157

Step-by-step explanation:

Given that:

The sample size n = 1200

The sample proportion of those that will vote for the Republican candidate is represented by $\hat p = \dfrac{x}{n}$

$\hat p = \dfrac{620}{1200}$

$\hat p =0.5167$

The null and the alternative hypothesis can be computed as:

$H_o: P=0.50 \\ \\ H_a :P>0.50$

The formula for the one-sample Z-test for the population proportion can be expressed as:

$Z = \dfrac{\hat p - P_o}{\sqrt{\dfrac{P_o(1-P_o)}{n}}}$

$Z = \dfrac{0.5167 - 0.5}{\sqrt{\dfrac{0.5(1-0.5)}{1200}}}$

$Z = \dfrac{0.0167}{\sqrt{\dfrac{0.5(0.5)}{1200}}}$

$Z = \dfrac{0.0167}{\sqrt{\dfrac{0.25}{1200}}}$

$Z = \dfrac{0.0167}{\sqrt{2.08333333\times10^{-4}}}$

Z = 1.157