Exercise 11-17 Algo Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical factor in determining the likelihood of an accident...

Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical factor in determining the likelihood of an accident occurring (Update, Virginia Department of Transportation, Winter 2000). One of the experts claims that driving conditions are dangerous if the variance of speeds exceeds 80 (mph)². On a heavily traveled highway, a random sample of 52 cars revealed a mean and a variance of speeds of 58.5 mph and 85.4(mph)², respectively.
(You may find it useful to reference the appropriate table: chi-square table or F table)

a.
Select the competing hypotheses to test if the variance of speeds exceeds 80 (mph)².

multiple choice 1

• 
  
  
  

  
  

  
  H
  ₀:
  σ
  ²
  ≤ 80;
  H
  
  _A
  :
  σ
  ²
  > 80

  
  

  
  
  
  


• 
  
  
  

  
  

  
  H
  ₀:
  σ
  ²
  ≥ 80;
  H
  
  _A
  :
  σ
  ²
  <>

  
  

  
  
  
  


• 
  
  
  

  
  

  
  H
  ₀:
  σ
  ²
  = 80;
  H
  
  _A
  :
  σ
  ²
  ≠ 80

  
  

  
  
  
  

b-1.
Find the
p-value.

multiple choice 2

• 
  
  
  

  
  

  
  p-value
  

  
  0.10
  

  
  

  
  

  
  
  
  


• 
  
  
  

  
  

  0.05
  

  
  p-value <>
  

  
  

  
  

  
  
  
  


• 
  
  
  

  
  

  0.025
  

  
  p-value <>
  

  
  

  
  

  
  
  
  


• 
  
  
  

  
  

  0.01
  

  
  p-value <>
  

  
  

  
  

  
  
  
  


• 
  
  
  

  
  

  
  p-value <>

  
  

  
  
  
  

b-2.
At the 10% significance level, can you conclude that driving conditions are dangerous on this highway?

multiple choice 3

• 
  
  
  

  
  

  Do not reject
  H
  ₀; we cannot conclude the variance of the speeds is greater than 80 mpg².

  
  

  
  
  
  


• 
  
  
  

  
  

  Reject
  H
  ₀; we can conclude the variance of the speeds is greater than 80 mpg².

  
  

  
  
  
  


• 
  
  
  

  
  

  Do not reject
  H
  ₀; we can conclude the variance of the speeds is greater than 80 mpg².

  
  

  
  
  
  


• 
  
  
  

  
  

  Reject
  H
  ₀; we cannot conclude the variance of the speeds is greater than 80 mpg²