# What is the alternative and null hypothesis for the following problem?

## A nutritionist has noticed a food farm ad stating the company's peanut butter has less fat that that produced by its competitor. She buys 11.8 ounce jars of each brand and measures the fat content of each. The 11 food farm jars had an average of 31.3 grams of fat, with a standard deviation of 1.8 grams.

Dec 23, 2017

Null:
"There is NO significant difference between the mean fat content of the new product compared to the mean of the general product fat content."
Alternate:
"There IS a significant difference between the mean fat content of the new product compared to the mean of the general product fat content."

#### Explanation:

Basically, you really want your null hypothesis to be the thing you want to disprove , because a statistical rejection of a hypothesis is more convincing than an inability to reject (we can NEVER really "accept" a hypothesis). That is probably the most basic error new statisticians make.

Similarly, don't get caught up in the numbers! They'll be used for the analysis, but they REALLY are NOT the desired answer. In this case, the question is whether a claim of less fat is valid or not. It doesn't matter what the fat content is - only the relative difference to the 'normal' products.

So, if we really think that the claim is true, we should state a Null Hypothesis that claims that it is NOT true. Then, if we can't reject it, they may be similar. But if we can reject it, then we are more confident that there is a difference between products.

Thus we arrive at the following statement:
"There is NO significant difference between the mean fat content of the new product compared to the mean of the general product fat content."

This still could be worded for similarity instead of difference - just be sure that you interpret your results consistently with your Null Hypothesis statement! the alternative is always the opposite of the Null - nothing more, nothing less.

"There is a significant difference between the mean fat content of the new product compared to the mean of the general product fat content."