Question

5.16 Identify hypotheses, Part II: Write the null and alternative hypotheses in words and then symbols for each of the following situations. (a) Since 2008, chain restaurants in California have been required to display calorie counts of each menu item. Prior to menus displaying calorie counts, the average calorie intake of diners at a restaurant was 1100 calories. After calorie counts started to be displayed on menus, a nutritionist collected data on the number of calories consumed at this restaurant from a random sample of diners. Do these data provide convincing evidence of a difference in the average calorie intake of a diners at this restaurant?

Answer 1

H₀: µ = 1100 vs. Hₐ: µ ≠ 1100.

Explanation:

A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.

It is a hypothesis of no difference.

It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.

For instance, H₀: µ = µ₀, where µ₀ is some null value or some claimed value.

Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.

The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.

It is also known as the research hypothesis and is denoted by Hₐ.

In this case the hypothesis can be defined as follows:

Null hypothesis:

H₀: The average calorie intake of a diner at this restaurant is 1100, i.e. µ = 1100.

Alternate hypothesis:

Hₐ: The average calorie intake of a diner at this restaurant is different from 1100, i.e. µ ≠ 1100.