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irakobra [83]
3 years ago
12

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
Mathematics
1 answer:
KATRIN_1 [288]3 years ago
3 0

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

     

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