Question

Apolitical researcher believes that the fraction p1 of Republicans strongly in favor of the death penalty is greater than the fraction p2 of Democrats strongly in favor of the death penalty. He acquired independent random samples of 200 Republicans and 200 Democrats and found 46 Republicans and 34 Democrats strongly favoring the death penalty. Does this evidence provide statistical support for the researcher’s belief? Use α = .05.

Answer 1

Answer:

The evidence provided does not statistically  support  the researcher’s belief

Step-by-step explanation:

From the question we are told that

   The sample size of each political party  is $n = 200$

   The  number of democrats that favor death penalty is  $k = 34$

    The  number of republicans that favor death penalty is  $u = 46$

Generally the sample proportion for Republicans is

       $\r p_1 = \frac{ 46}{200}$

        $\r p_1 = 0.23$

Generally the sample proportion for Democrats is

        $\r p_2 = \frac{ 34}{200}$

        $\r p_1 = 0.17$

The  null hypothesis is  $H_o : \r p _1 = \r p_2$

The  alternative hypothesis is $H-_1 : \r p_1 > \r p_2$

  Generally the pooled population proportion is evaluated as

        $\r p = \frac{ k + u }{n + n }$

         $\r p = \frac{ 34 + 46 }{200 + 200 }$

        $\r p = 0.2$

The test statistics is evaluated as

           $t = \frac{ \r p _1 - \r p_2 }{\sqrt{ \r p (1 - \r p ) [\frac{1}{n} +\frac{1}{n} ]} }$

          $t = 1.5$

The  p-value is obtained from the z-table  the value is  

      $p-value = P(Z> 1.50 ) = 0.066807$

=>   $p-value = 0.066807$

Given that $p-value > \alpha$ then we fail to  reject the null hypothesis this mean that there is no sufficient evidence to support the researcher’s belief