Question

YThe Pew Research Center conducted a survey of 1007 adults and found that 85% of them know what Twitter is. Find a 90% confidence interval for the proportion of all adults who know what Twitter is. Also find the margin of error. Round all of your answers to four decimal places.

Answer 1

Answer:

The 90% confidence interval is   $0.8315 < p < 0.8685$

Step-by-step explanation:

From the question we are told that

   The sample size is n =  1007  

    The sample proportion is  $\^ p = 0.85$

From the question we are told the confidence level is  90% , hence the level of significance is    

      $\alpha = (100 - 90 ) \%$

=>   $\alpha = 0.10$

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

   $Z_{\frac{\alpha }{2} } = 1.645$

Generally the margin of error is mathematically represented as  

      $E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p(1- \^ p)}{n}}$

=>   $E =1.645 * \sqrt{\frac{0.85 (1- 0.85 )}{1007}}$

=>   $E = 0.0185$    

Generally 90% confidence interval is mathematically represented as  

      $\^ p -E < p < \^ p +E$

=>  $0.85 -0.0185 < p < 0.85 + 0.0185$

=>  $0.8315 < p < 0.8685$