Question

Travel time data is collected on an arterial. With 30 runs, an average travel time of 152 seconds is computed over the 2.0 miles length, with a computed standard deviation of 17.3 seconds.
Required:
a. Compute 95% confidence bounds on your estimate of the mean.
b. Was it necessary to make any assumption about the shape of the travel-time distribution?

Answer 1

Answer:

a

 The 95% confidence bounds is  $145.80 < \mu < 158.19$

b

It was not necessary to make any assumption about the shape of the travel  time distribution

Step-by-step explanation:

From the question we are told that

 The sample size is  n =  30  

  The sample mean  is  $\=x = 152$

   The standard deviation is  $\sigma = 17.3 \ second$

From the question we are told the confidence level is  95% , hence the level of significance is    

      $\alpha = (100 - 95 ) \%$

=>   $\alpha = 0.05$

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

   $Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as  

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

=>    $E = 1.96 * \frac{17.3 }{\sqrt{30} }$

=>     $E = 6.19$  

Generally 95% confidence bounds  is mathematically represented as  

      $\= x -E < \mu < \=x +E$

=>  $152 -6.19 < \mu < 152 -6.19$

=> $145.80 < \mu < 158.19$

This 95% confidence bounds show that there is 95% confidence that the true mean lies within this bound hence there is it was not necessary to make any assumption about the shape of the travel  time distribution