Question

For each of the following scenarios, develop a testable hypothesis.
a. Scenario 1. Kelly and Jack are playing in the park. Jack rolls a marble
down the small playground slide. Kelly proposes the idea that the marble
would travel at a faster pace if it is rolled down the longer slide.
b. Scenario 2. Andy’s nightly chores include washing the family dishes. His
mother tends to cook everything that she prepares a bit too long. Because
of this, Andy spends a lot of swear, effort, and time washing the dishes.
He sees a commercial on televisions that claims that brand X dishwashing
detergent cuts through grease better than its competitor brand Y.
c. Scenario 3. Ali’s favorite food is microwave popcorn. She lives microwave
popcorn so much that she can’t stand to waste the un-popped kernels in
the bottom of the bag. The next time Ali goes to the grocery store she
buys all the brands of microwave popcorn that the store has.

Answer 1

Scenario 1
Let μ1 be the average speed of the marble on the small slide  
Let μ2 be the average speed of the marble on the long slide  
Then the null and alternative hypothesis are  
Ho : μ₁ = μ₂  
Ha : μ₁ < μ₂               (Since they have to test if the speed is higher on the long slide)
  
Scenario 2
Let μx be the average time Andy spends dishwashing using Brand X  
Let μy be the average time Andy spends dishwashing using Brand Y  
Then the null and alternative hypothesis are  
Ho : μ_x = μ_y  
Ha : μ_x < μ_y              (Since Andy has to test if the Brand X is better than Brand Y)
                                  (So the time for washing using X should be less than that for Y)
  
Scenario 3  
Let Ali buy n brands of microwave popcorn  
Let Pi be the proportion of un-popped kernels in the i-th brand of microwave popcorn  
Pi = number of unpopped kernels / total number of kernels in the bag  
Then the null and alternative hypothesis are  
Ho : Proportion of un-popped kernels is the same for all n brands of microwave popcorn  
Ha : Atleast one brand of microwave popcorn differs from the others in the proportion of un-popped kernels