Question

A recent debate about where in the United States skiers believe the skiing is best prompted the following survey. Test to see if the best ski area is independent of the level of the skier. (Use a significance level of 0.05.)

U.S. Ski Area	Beginner	Intermediate	Advanced
Tahoe	20	28	39
Utah	11	29	62
Colorado	11	41	52

• Part (a)

  State the null hypothesis.

  Ski area is dependent on the level of the skier.Ski area is independent of the level of the skier.    

• Part (b)

  State the alternative hypothesis.

  Ski area is independent of the level of the skier.Ski area is dependent on the level of the skier.    

• Part (c)

  What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)
  (No Response)

• Part (d)

  State the distribution to use for the test.

  χ²₂

  t₄

      

  χ²₄

  t₂

• Part (e)

  What is the test statistic? (Round your answer to two decimal places.)
  (No Response)

• Part (f)

  What is the p-value? (Round your answer to four decimal places.)
  (No Response)
  
  Explain what the p-value means for this problem.

  If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.    If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.

• Part (g)

  Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.

• Part (h)

  Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write the appropriate conclusion.(i) Alpha:
  α = (No Response)
  
  (ii) Decision:

  reject the null hypothesisdo not reject the null hypothesis    

  
  (iii) Reason for decision:

  Since α < p-value, we do not reject the null hypothesis.Since α > p-value, we reject the null hypothesis.    Since α > p-value, we do not reject the null hypothesis.Since α < p-value, we reject the null hypothesis.

  
  (iv) Conclusion:

  The best ski area and level of skier are independent.The best ski area and level of skier are not independent.  

Answer 1

Part (a)

State the null hypothesis.

Ski area is independent of the level of the skier.

Part (b)

State the alternative hypothesis.

Ski area is dependent on the level of the skier.  

Part (c)

What are the degrees of freedom?

Answer : degrees of freedom =4

Part (d)

State the distribution to use for the test.

χ²₄

• Part (e)

• 

  

• What is the test statistic? (Round your answer to two decimal places.)

• Part (f)

  What is the p-value? (Round your answer to four decimal places.)
  p-value = 0.0286.
• Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write the appropriate conclusion.(i) Alpha:
  α = 0.05
  
  (ii) Decision:

  reject the null hypothesis

  
  (iii) Reason for decision:

  Since α < p-value, we reject the null hypothesis.

  
  (iv) Conclusion:

  .The best ski area and level of skier are not independent.