Question

In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 75% of adults say that it is morally wrong to not report all income on tax returns.a. What is the null and alternative hypothesis?b. What is the test statistic?c. What is the P-value?d. What is the Conclusion?

Answer 1

Answer:

a

 

   The  null hypothesis is  $H_o : p = 0.75$

  The  alternative  hypothesis is  $H_a : p \ne 0.75$

b

   $t = 2.51$

c

   $p-value = 0.01207$

d

 There no sufficient evidence to conclude that 75% of adults say that it is morally wrong to not report all income on tax returns

Step-by-step explanation:

From the question we are told that

    The  sample  size is  $n = 745$

     The  number that said it is morally wrong is  $k = 589$

       The  level of significance is  $\alpha = 0.01$

        The population proportion is $p = 0.75$

Generally the sample  proportion is mathematically represented as

        $\r p = \frac{k}{n}$

=>     $\r p = \frac{589}{745}$

=>     $\r p = 0.79$

 The  null hypothesis is  $H_o : p = 0.75$

  The  alternative  hypothesis is  $H_a : p \ne 0.75$

The  standard error is mathematically represented as

     $SE = \sqrt{\frac{p(1-p)}{n} }$

=>    $SE = \sqrt{\frac{0.75(1-0.75)}{745} }$

=>    $SE =0.0159$

Generally the test statistics is mathematically represented as

      $t = \frac{\r p - p }{SE}$

=>   $t = \frac{0.79 - 0.75 }{0.0159}$

=>    $t = 2.51$

Generally the p-value is  mathematically represented as

        $p-value = 2 * P(Z > 2.51)$

From the the z-table  

            $P(Z > 2.51) = 0.0060366$

=>   $p-value = 2 * 0.0060366$

=>   $p-value = 0.01207$

From the calculation  $p-value >\alpha$

    Hence we fail to reject the null hypothesis

Thus there no sufficient evidence to conclude that 75% of adults say that it is morally wrong to not report all income on tax returns