Question

Job Interviews In a Harris poll of 514 human resource professionals, 45.9% said that body piercings and tattoos were big grooming red flags. Construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big grooming red flags. Group of answer choices 0.42

Answer 1

Answer:

The 99% confidence interval is  $0.4023 < p < 0.5157$

Step-by-step explanation:

From the question we are told that

       The sample size is  n = 514

        The sample proportion is  $\^ p = 0.459$

       

From the question we are told the confidence level is  99% , hence the level of significance is    

      $\alpha = (100 - 99 ) \%$

=>   $\alpha = 0.01$

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

   $Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as  

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

=>   $E =2.58 * \sqrt{\frac{0.459 (1- 0.459)}{514} }$

=>    $E =0.0567$

Generally 99% confidence interval is mathematically represented as  

      $0.459 -0.0567 < p < 0.459 + 0.0567$

=>    $0.4023 < p < 0.5157$