Question

Suppose a random sample of 50 college students are asked to measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at the college is found to be 21.709 to 25.091 cm. If a 99% confidence interval were calculated instead, how would it differ from the 95% confidence interval

Answer 1

Answer:

A  99% confidence interval  will be wider than a 95% confidence interval

Step-by-step explanation:

From the question we are told that

  The  95% confidence interval for for the mean foot length for students at the college is found to be 21.709 to 25.091 cm

Generally the width of a confidence interval is dependent on the margin of error.

Generally the margin of error is mathematically represented as  

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

From the above equation we see that

          $E \ \ \alpha \ \ Z_{\frac{\alpha }{2} }$

Here  $Z_{\frac{\alpha }{2} }$  is the critical value of the half of the level of significance and this value  increase as the confidence level increase

Now if a  99% confidence level is  used , it then means that the value of  

 $Z_{\frac{\alpha }{2} }$  will increase, this in turn will increase  the margin of error and in turn this will increase the width of the confidence interval

Hence a 99% confidence interval  will be wider than a 95% confidence interval