Question

question 12

gaetan wanted to test a new stain remover to see if it was more effective in removing grease stains from his pants.

which of the following would be the null hypothesis in gaetans experiment?

• there will be no difference in the effectiveness of the new stain remover compared to the old one.
• the difference between the new stain remover and the old one will be significant.
• the new stain removers will be more effective than the old one.
• the new stain remover could be more or less effective than the old one.

Explanation:

Define the null hypothesis concept

The null hypothesis (typically denoted as \(H_0\)) is a fundamental concept in statistics and experimental design. It represents the default position or baseline assumption that there is no effect, no change, or no difference between the groups or treatments being compared.

Analyze Gaetan's experiment

Gaetan is testing a new stain remover to see if it is more effective at removing grease stains compared to an old or existing method.

• The alternative hypothesis (\(H_1\)) is what the researcher hopes to support: that the new stain remover is indeed more effective than the old one.
• The null hypothesis (\(H_0\)) must state the opposite of the effect being tested, asserting that the new treatment has no special effect. Therefore, it states that there is no difference in effectiveness between the new stain remover and the old one.

Evaluate the given options

• Option 1: "There will be no difference in the effectiveness of the new stain remover compared to the old one." This directly aligns with the definition of a null hypothesis (no difference/no effect).
• Option 2: "The difference between the new stain remover and the old one will be significant." This describes an alternative hypothesis where an effect is present.
• Option 3: "The new stain removers will be more effective than the old one." This is a directional alternative hypothesis.
• Option 4: "The new stain remover could be more or less effective than the old one." This describes a non-directional alternative hypothesis or general uncertainty, not a null statement of "no difference."

Answer:

• There will be no difference in the effectiveness of the new stain remover compared to the old one. (Correct answer)
• The difference between the new stain remover and the old one will be significant.
• The new stain removers will be more effective than the old one.
• The new stain remover could be more or less effective than the old one.