Question

krusty was told that a new itching powder claims to cause 50% longer lasting itches. interested in this product, he buys the itching powder and compares it to his usual product. one test subject (a) is sprinkled with the new experimental itching powder. another test subject (b) was sprinkled with the original itching powder. his results are below.
subject a subject b
number of minutes itched 30 minutes 45 minutes

1. identify the independent variable.
2. dependent variable.
3. what should krusty’s conclusion be? use data (numbers) to support your answer.
4. how could krusty improve his experiment?

Explanation:

Step1: Identify independent variable

The variable that is being changed or manipulated is the type of itching - powder. So, the independent variable is the type of itching - powder (new and original).

Step2: Identify dependent variable

The variable that is being measured is the time the test subjects itch. So, the dependent variable is the number of minutes the test subjects itch.

Step3: Evaluate conclusion support

To support the conclusion that the new powder causes 50% longer - lasting itches, we need to calculate the percentage increase in itching time. The original powder (Subject B) itched for 45 minutes and the new powder (Subject A) itched for 30 minutes. The formula for percentage increase is $\frac{\text{New Value}-\text{Original Value}}{\text{Original Value}}\times100\%$. Here, the calculation would be $\frac{45 - 30}{30}\times100\%=\frac{15}{30}\times100\% = 50\%$. But this is in the wrong direction as the new powder has a shorter itching time. So, the data does not support the conclusion.

Step4: Suggest improvement

To improve the experiment, Krusty could use a larger sample size of test subjects to get more reliable results. He could also control for other factors such as the amount of powder applied, the skin type of the test subjects, and the location on the body where the powder is applied.

Answer:

1. Independent Variable: Type of itching - powder (new and original)
2. Dependent Variable: Number of minutes the test subjects itch
3. The data does not support Krusty's conclusion. Calculating the percentage increase in itching time using the formula $\frac{\text{New Value}-\text{Original Value}}{\text{Original Value}}\times100\%$ gives a 50% increase in itching time for the original powder compared to the new powder, which is the opposite of what Krusty claims.
4. Krusty could improve the experiment by using a larger sample size, controlling for the amount of powder applied, and accounting for differences in test - subject skin type and application location.