Question

If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance, what are the alternative hypothesis and rejection region?

Answer 1

Answer:

The alternative hypothesis is

      $H_a : p_1 \ne \ p_2$

The rejection region is the region outside the interval

         $-1.96 < z_{critical} < 1.96$

Step-by-step explanation:

From the question we are told that

    The significance level is  $\alpha = 0.05$

     The null hypothesis is  $H_o : p_1 = p_2$

      The  alternative hypothesis is  $H_a : p_1 \ne \ p_2$

Generally from the normal distribution table the critical value  of  $\frac{\alpha }{2}$ is  

   $Z_{\frac{\alpha }{2} } =  1.96$

Hence the rejection region is the region outside the interval $-1.96 < z_{critical} < 1.96$

Answer 2

The alternative hypothesis is, $H _a; \ P_1\neq P_2$ .

And the rejection region is the region outside the interval is $-1.96< Z_c_r_i_t_i_c_a_l <1.96$ .

Given that,

If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance.

We have to determine,

What is the alternative hypothesis and rejection region?

According to the question,

The significance level is,  $\alpha = 5 \ percent = 0.05$

The null hypothesis is $H_0 ; P_1 = P_2$

The alternative hypothesis is, $H _a; \ P_1\neq P_2$

In the normal distribution table, the critical value $\dfrac{\alpha}{2}$ is,

$Z _\frac{\alpha}{2} = 1.96$

Hence, the rejection region is the region outside the interval is $-1.96< Z_c_r_i_t_i_c_a_l <1.96$ .

To know more about the Hypothesis click the link given below.

https://brainly.com/question/21620502