Question

The difference between teenage female and male depression rates estimated from two samples is 0.07. The estimated standard error of the sampling distribution is 0.03. What is the 95% confidence interval

Answer 1

Answer:

The 95%  confidence interval is  $0.0112 < \mu_m - \mu_f < 0.1288$

Step-by-step explanation:

From  the question we are told that  

      The  sample  mean difference is  $\= x_m - \= x_f = 0.07$

       The  standard error  is  SE  =  0.03

Given that the confidence interval is  95% then the level of significance is mathematically evaluated as

               $\alpha = 100 - 95$

               $\alpha = 5\%$

               $\alpha =0.05$

Next  we obtain the critical value of  $\frac{\alpha }{2}$ from the normal distribution table, the value is  $Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

         $E = Z_{\frac{ \alpha }{2} } * SE$

substituting values

         $E = 1.96 * 0.03$

         $E = 0.0588$

The 95% confidence interval  is mathematically represented as

      $(\= x_m - \= x_f ) - E < \mu_m - \mu_f$

substituting values

     $0.07 - 0.0588 < \mu_m - \mu_f$

    $0.0112 < \mu_m - \mu_f < 0.1288$