Question

SAT scores: A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 433 . Assume the population standard deviation is 115 .
(a) Construct a 99 % confidence interval for the mean mathematics SAT score for the entering freshman class. Round the answer to the nearest whole number.

Answer 1

Answer:

The 99% confidence interval is  $403.33 <  \mu < 462.67$  

Step-by-step explanation:

From the question we are told that

  The sample size is  n  =  100

   The sample mean is  $\= x = 433$

    The standard deviation is $\sigma = 115$

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  

      $E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }$

=>   $E = 2.58 *  \frac{115 }{\sqrt{100} }$

=>   $E = 29.67$

Generally 99% confidence interval is mathematically represented as  

      $\= x -E <  \mu <  \=x  +E$

=>    $433 -29.67 <  \mu < 433 + 29.67$    

=>    $403.33 <  \mu < 462.67$